&]\c @`sddlmZmZmZddlZddlZddlmZm Z ddl m Z ddl m Z ddl m Z ddljZddljjZddlmZddlmZmZd d lmZd d lmZmZd d l m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(d d l)m*Z*m+Z+m,Z,m-Z-m.Z.y ej/Z/Wne0k rrej1Z/nXde&fdYZ2e2ddddZ3de&fdYZ4e4ddddZ5ej6dej7Z8ej9e8Z:dZ;dZ<dZ=dZ>dZ?dZ@dZAdZBd e&fd!YZCeCdd"ZDd#e&fd$YZEeEdddd%ZFd&e&fd'YZGeGdej7 d(d)ej7d(dd*ZHd+e&fd,YZIeIddd)d-dd.ZJd/eKfd0YZLd1eMfd2YZNd3ZOd4ZPd5e&fd6YZQeQddd)d-dd7ZRd8e&fd9YZSeSdddd:ZTd;e&fd<YZUeUddd)d-dd=ZVd>e&fd?YZWeWdddd@ZXdAe&fdBYZYeYddddCZZdDeWfdEYZ[e[ddddFZ\dGe&fdHYZ]e]ddIZ^dJe&fdKYZ_e_ddddLZ`dMe&fdNYZaeaddddOZbdPe&fdQYZcecdej7 d)ej7ddRZddSe&fdTYZeeeddUZfdVe&fdWYZgegddXZhdYe&fdZYZieidddd[Zjd\e&fd]YZkekdd^Zld_e&fd`YZmemddddaZndbe&fdcYZoeodddddZpdee&fdfYZqeqddddgZrdhe&fdiYZsesddddjZtdke&fdlYZueuddddmZvdne&fdoYZwewddddpZxdqe&fdrYZyeyddddsZzdte&fduYZ{e{d)dddvZ|dwZ}dxeyfdyYZ~e~ddddzZd{Zd|e{fd}YZed)ddd~Zde&fdYZeddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddZdZde&fdYZeddddZdefdYZeddddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddZde&fdYZeddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddZde&fdYZeddd)d-ddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddZde&fdYZeddddZde&fdYZeddd)d-ddZde&fdYZeddZde&fdYZeddZde&fdYZeddddZde&fdYZed)dddZde&fdYZeddZde&fdYZeddZde&fdYZeddZde&fdYZeddddZdZde&fdYZeddddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddZde&fdYZeddddZde&fdYZeddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddZde&fdYZeddZde&fdYZedd-ddZde&fdYZeddddZde&fdYZeddZde&fdYZeddd)d-ddZde&fd YZedddd Zd e&fd YZedd Zde&fdYZeddd)d-ddZde&fdYZeddddZde&fdYZeddZde&fdYZeddddZde&fdYZeddddZde&fdYZeddd)d-dd Zd!e&fd"YZedd#Zd$e&fd%YZeddd)d-dd&Zd'e&fd(YZeddd)d-dd)Zd*e&fd+YZedddd,Zd-e&fd.YZedd/Zd0e&fd1YZedd2Zd3eLfd4YZd5e&fd6YZeddd)d-dd7Zd8e&fd9YZedd:Zedej7 d)ej7dd;Zd<efd=YZedddd>Zd?e&fd@YZeddd)dej7ddAZdBe&fdCYZeddDZdEe&fdFYZeddddGZdHe&fdIYZ e ddJdKdLZ dMZ dNe&fdOYZ e ddPdKdQddd)d-Z dRe&fdSYZeejZe!ee&\ZZeedRgZdS(Ti(tdivisiontprint_functiontabsolute_importN(textend_notes_in_docstringtreplace_notes_in_docstring(toptimize(t integrate(t interpolate(t broadcast_to(t _lazyselectt _lazywherei(t_stats(ttukeylambda_variancettukeylambda_kurtosis(tget_distribution_namest _kurtosist _ncx2_cdft _ncx2_log_pdft _ncx2_pdft rv_continuoust_skewtvalarray(t_XMINt_EULERt_ZETA3t_XMAXt_LOGXMAXt ksone_gencB`s;eZdZdZdZdZdZdZRS(sGeneral Kolmogorov-Smirnov one-sided test. This is the distribution of the one-sided Kolmogorov-Smirnov (KS) statistics :math:`\sqrt{n} D_n^+` and :math:`\sqrt{n} D_n^-` for a finite sample size ``n`` (the shape parameter). %(before_notes)s Notes ----- :math:`\sqrt{n} D_n^+` and :math:`\sqrt{n} D_n^-` are given by .. math:: D_n^+ &= \text{sup}_x (F_n(x) - F(x)),\\ D_n^- &= \text{sup}_x (F(x) - F_n(x)),\\ where :math:`F` is a CDF and :math:`F_n` is an empirical CDF. `ksone` describes the distribution under the null hypothesis of the KS test that the empirical CDF corresponds to :math:`n` i.i.d. random variates with CDF :math:`F`. %(after_notes)s See Also -------- kstwobign, kstest References ---------- .. [1] Birnbaum, Z. W. and Tingey, F.H. "One-sided confidence contours for probability distribution functions", The Annals of Mathematical Statistics, 22(4), pp 592-596 (1951). %(example)s cC`stj|| S(N(tscut _smirnovp(tselftxtn((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_pdfNscC`stj||S(N(Rt _smirnovc(RRR ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_cdfQscC`stj||S(N(tsctsmirnov(RRR ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_sfTscC`stj||S(N(Rt _smirnovci(RtqR ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_ppfWscC`stj||S(N(R$tsmirnovi(RR(R ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_isfZs(t__name__t __module__t__doc__R!R#R&R)R+(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR(s %    tagtnametksonet kstwobign_gencB`s;eZdZdZdZdZdZdZRS(sKolmogorov-Smirnov two-sided test for large N. This is the asymptotic distribution of the two-sided Kolmogorov-Smirnov statistic :math:`\sqrt{n} D_n` that measures the maximum absolute distance of the theoretical CDF from the empirical CDF (see `kstest`). %(before_notes)s Notes ----- :math:`\sqrt{n} D_n` is given by .. math:: D_n = \text{sup}_x |F_n(x) - F(x)| where :math:`F` is a CDF and :math:`F_n` is an empirical CDF. `kstwobign` describes the asymptotic distribution (i.e. the limit of :math:`\sqrt{n} D_n`) under the null hypothesis of the KS test that the empirical CDF corresponds to i.i.d. random variates with CDF :math:`F`. %(after_notes)s See Also -------- ksone, kstest References ---------- .. [1] Marsaglia, G. et al. "Evaluating Kolmogorov's distribution", Journal of Statistical Software, 8(18), 2003. %(example)s cC`stj| S(N(Rt_kolmogp(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s tj|S(N(Rt_kolmogc(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s tj|S(N(R$t kolmogorov(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`s tj|S(N(Rt _kolmogci(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s tj|S(N(R$tkolmogi(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+s(R,R-R.R!R#R&R)R+(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR2as #    t kstwobignicC`stj|d dtS(Nig@(tnptexpt _norm_pdf_C(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _norm_pdfscC`s|d dtS(Nig@(t_norm_pdf_logC(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _norm_logpdfscC`s tj|S(N(R$tndtr(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _norm_cdfscC`s tj|S(N(R$tlog_ndtr(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _norm_logcdfscC`s tj|S(N(R$tndtri(R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _norm_ppfscC`s t| S(N(R@(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_norm_sfscC`s t| S(N(RB(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _norm_logsfscC`s t| S(N(RD(R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _norm_isfstnorm_gencB`seZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z eed d dZRS(sA normal continuous random variable. The location (``loc``) keyword specifies the mean. The scale (``scale``) keyword specifies the standard deviation. %(before_notes)s Notes ----- The probability density function for `norm` is: .. math:: f(x) = \frac{\exp(-x^2/2)}{\sqrt{2\pi}} for a real number :math:`x`. %(after_notes)s %(example)s cC`s|jj|jS(N(t _random_statetstandard_normalt_size(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_rvsscC`s t|S(N(R<(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s t|S(N(R>(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_logpdfscC`s t|S(N(R@(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s t|S(N(RB(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_logcdfscC`s t|S(N(RE(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`s t|S(N(RF(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_logsfscC`s t|S(N(RD(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s t|S(N(RG(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+scC`sdS(Ngg?(gg?gg((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`sdtjdtjdS(Ng?ii(R9tlogtpi(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_entropystnotess This function uses explicit formulas for the maximum likelihood estimation of the normal distribution parameters, so the `optimizer` argument is ignored. cK`s|jdd}|jdd}|dk rK|dk rKtdntj|}|dkru|j}n|}|dkrtj||dj}n|}||fS(Ntfloctfscales3All parameters fixed. There is nothing to optimize.i(tgettNonet ValueErrorR9tasarraytmeantsqrt(RtdatatkwdsRTRUtloctscale((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pytfits   (R,R-R.RLR!RMR#RNR&ROR)R+R RRRRR`(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRHs            tnormt alpha_gencB`sDeZdZejZdZdZdZdZ dZ RS(sAn alpha continuous random variable. %(before_notes)s Notes ----- The probability density function for `alpha` is: .. math:: f(x, a) = \frac{1}{x^2 \Phi(a) \sqrt{2\pi}} * \exp(-\frac{1}{2} (a-1/x)^2) where :math:`\Phi` is the normal CDF, :math:`x > 0`, and :math:`a > 0`. `alpha` takes ``a`` as a shape parameter. %(after_notes)s %(example)s cC`s(d|dt|t|d|S(Ng?i(R@R<(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!4scC`s6dtj|t|d|tjt|S(Nig?(R9RPR>R@(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM8scC`st|d|t|S(Ng?(R@(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#;scC`s(dtj|tj|t|S(Ng?(R9RYR$RCR@(RR(R/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)>scC`stjgdtjgdS(Ni(R9tinftnan(RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR As( R,R-R.Rt_open_support_maskt _support_maskR!RMR#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRbs     talphat anglit_gencB`s;eZdZdZdZdZdZdZRS(sAn anglit continuous random variable. %(before_notes)s Notes ----- The probability density function for `anglit` is: .. math:: f(x) = \sin(2x + \pi/2) = \cos(2x) for :math:`-\pi/4 \le x \le \pi/4`. %(after_notes)s %(example)s cC`stjd|S(Ni(R9tcos(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!\scC`stj|tjddS(Nig@(R9tsinRQ(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#`scC`s!tjtj|tjdS(Ni(R9tarcsinR[RQ(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)cscC`sGdtjtjddddtjddtjtjddfS( Ngig?iii`ii(R9RQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR fscC`sdtjdS(Nii(R9RP(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRis(R,R-R.R!R#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRhHs     itbtanglitt arcsine_gencB`s;eZdZdZdZdZdZdZRS(s An arcsine continuous random variable. %(before_notes)s Notes ----- The probability density function for `arcsine` is: .. math:: f(x) = \frac{1}{\pi \sqrt{x (1-x)}} for :math:`0 < x < 1`. %(after_notes)s %(example)s cC`s dtjtj|d|S(Ng?i(R9RQR[(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s!dtjtjtj|S(Ng@(R9RQRkR[(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stjtjd|dS(Ng@(R9RjRQ(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s(d}d}d}d}||||fS( Ng?g?iigg@g?g((Rtmutmu2tg1tg2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s cC`sdS(Ngο((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs(R,R-R.R!R#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRnps     g?tarcsinet FitDataErrorcB`seZdZRS(cC`s(djd|d|d|f|_dS(NsInvalid values in `data`. Maximum likelihood estimation with {distr!r} requires that {lower!r} < x < {upper!r} for each x in `data`.tdistrtlowertupper(tformattargs(RRuRvRw((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt__init__s (R,R-Rz(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRtstFitSolverErrorcB`seZdZRS(cC`s,d}||jdd7}|f|_dS(Ns1Solver for the MLE equations failed to converge: s t(treplaceRy(Rtmesgtemsg((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRzs(R,R-Rz(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR{scC`s3tj||}||| tj|}|S(N(R$tpsi(R/RlR ts1tpsiabtfunc((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _beta_mle_ascC`s[|\}}tj||}||| tj|||| tj|g}|S(N(R$R(tthetaR Rts2R/RlRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _beta_mle_abs  tbeta_gencB`sheZdZdZdZdZdZdZdZdZ e e dd d Z RS( sA beta continuous random variable. %(before_notes)s Notes ----- The probability density function for `beta` is: .. math:: f(x, a, b) = \frac{\Gamma(a+b) x^{a-1} (1-x)^{b-1}} {\Gamma(a) \Gamma(b)} for :math:`0 < x < 1`, :math:`a > 0`, :math:`b > 0`, where :math:`\Gamma` is the gamma function (`scipy.special.gamma`). `beta` takes :math:`a` and :math:`b` as shape parameters. %(after_notes)s %(example)s cC`s|jj|||jS(N(RItbetaRK(RR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`stj|j|||S(N(R9R:RM(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`sEtj|d| tj|d|}|tj||8}|S(Ng?(R$txlog1pytxlogytbetaln(RRR/RltlPx((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs+cC`stj|||S(N(R$tbtdtr(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stj|||S(N(R$tbtdtri(RR(R/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s|d||}||d||d||d}d||tjd||||d||}d|d|ddd||dd|d||d|}|||||d||d}||||fS(Ng?g@ig@ii(R9R[(RR/RltmntvarRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s &7F&c`sdt|t|fd}tj|d\}}tt|j|d||fS(Nc`s|\}}d||tj||d||dtj||}|d|dd|d|d|dd|||d}|||||d||d}|d9}||gS(Niiii(R9R[(RR/Rltsktku(RqRr(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs  @B& g?Ry(g?g?(RRRtfsolvetsuperRt _fitstart(RR\RR/Rl((RqRrs=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs   RSs In the special case where both `floc` and `fscale` are given, a `ValueError` is raised if any value `x` in `data` does not satisfy `floc < x < floc + fscale`. cO`s|jddp3|jddp3|jdd}|jddpi|jddpi|jdd}|jdd}|jdd}|dks|dkrtt|j|||S|dk r|dk rtd ntj|||}tj|d ks,tj|d krKt d d |d||n|j }|dk so|dk r?|dk r|} d |}d |}n|} | |d |} t j t | d| t|tj|jfdt\} } } }| d krtd|n| d } |dk r | | } } q ntj|j}tj| j}|d ||jdd d }||} d ||} t j t| | gdt|||fdt\} } } }| d krtd|n| \} } | | ||fS(Ntf0tfatfix_atf1tfbtfix_bRTRUs3All parameters fixed. There is nothing to optimize.iiRRvRwRyt full_outputR~tddof(RVRWRRR`RXR9traveltanyRtRZRRRtlenRPtsumtTrueR{R$tlog1pRR(RR\RyR]RRRTRUtxbarRlR/RtinfotierR~RRtfac((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR` sV$$ *     $   "   ( R,R-R.RLR!RMR#R)R RRRR`(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs        Rt betaprime_gencB`sDeZdZejZdZdZdZdZ dZ RS(sA beta prime continuous random variable. %(before_notes)s Notes ----- The probability density function for `betaprime` is: .. math:: f(x, a, b) = \frac{x^{a-1} (1+x)^{-a-b}}{\beta(a, b)} for :math:`x > 0`, :math:`a > 0`, :math:`b > 0`, where :math:`\beta(a, b)` is the beta function (see `scipy.special.beta`). `betaprime` takes ``a`` and ``b`` as shape parameters. %(after_notes)s %(example)s cC`sQ|j|j}}tj|d|d|}tj|d|d|}||S(Ntsizet random_state(RKRItgammatrvs(RR/Rltsztrndmtu1tu2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`stj|j|||S(N(R9R:RM(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s8tj|d|tj|||tj||S(Ng?(R$RRR(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`stj|||d|S(Ng?(R$tbetainc(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s*|dkr0tj|dk||dtjS|dkrptj|dk||d|d|dtjS|dkrtj|dk||d|d|d|d|dtjS|dkr tj|dk||d|d|d|d|d|d|dtjStdS( Ng?ig@ig@ig@i(R9twhereRctNotImplementedError(RR R/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_munps$      +    ( R,R-R.RReRfRLR!RMR#R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRos     t betaprimet bradford_gencB`s>eZdZdZdZdZddZdZRS(s`A Bradford continuous random variable. %(before_notes)s Notes ----- The probability density function for `bradford` is: .. math:: f(x, c) = \frac{c}{\log(1+c) (1+cx)} for :math:`0 < x < 1` and :math:`c > 0`. `bradford` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`s|||dtj|S(Ng?(R$R(RRtc((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stj||tj|S(N(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stj|tj||S(N(R$texpm1R(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)stmvcC`stjd|}||||}|d|d|d|||}d}d}d|krtjdd||d|||dd||||dd}|tj|||dd|d||dd|}nd |kr|d|d|d|d d d||||d |dd|||d|d d|d}|d|||dd|d}n||||fS(Ng?g@itsi i iitkiiii(R9RPRWR[(RRtmomentsRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s& KB n)cC`s,tjd|}|dtj||S(Nig@(R9RP(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs(R,R-R.R!R#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs     tbradfordtburr_gencB`s;eZdZejZdZdZdZdZ RS(sA Burr (Type III) continuous random variable. %(before_notes)s See Also -------- fisk : a special case of either `burr` or `burr12` with ``d=1`` burr12 : Burr Type XII distribution Notes ----- The probability density function for `burr` is: .. math:: f(x, c, d) = c d x^{-c-1} (1+x^{-c})^{-d-1} for :math:`x > 0` and :math:`c, d > 0`. `burr` takes :math:`c` and :math:`d` as shape parameters. This is the PDF corresponding to the third CDF given in Burr's list; specifically, it is equation (11) in Burr's paper [1]_. %(after_notes)s References ---------- .. [1] Burr, I. W. "Cumulative frequency functions", Annals of Mathematical Statistics, 13(2), pp 215-232 (1942). %(example)s cC`s+|||| dd|| | dS(Ng?i((RRRtd((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`sd|| | S(Ni((RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s|d|dd|S(Ngi((RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s*d||}|tjd|||S(Ng?(R$R(RR RRtnc((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs( R,R-R.RReRfR!R#R)R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs "    tburrt burr12_gencB`s_eZdZejZdZdZdZdZ dZ dZ dZ dZ RS( sA Burr (Type XII) continuous random variable. %(before_notes)s See Also -------- fisk : a special case of either `burr` or `burr12` with ``d=1`` burr : Burr Type III distribution Notes ----- The probability density function for `burr` is: .. math:: f(x, c, d) = c d x^{c-1} (1+x^c)^{-d-1} for :math:`x > 0` and :math:`c, d > 0`. `burr12` takes ``c`` and ``d`` as shape parameters for :math:`c` and :math:`d`. This is the PDF corresponding to the twelfth CDF given in Burr's list; specifically, it is equation (20) in Burr's paper [1]_. %(after_notes)s The Burr type 12 distribution is also sometimes referred to as the Singh-Maddala distribution from NIST [2]_. References ---------- .. [1] Burr, I. W. "Cumulative frequency functions", Annals of Mathematical Statistics, 13(2), pp 215-232 (1942). .. [2] https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/b12pdf.htm %(example)s cC`stj|j|||S(N(R9R:RM(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!JscC`sGtj|tj|tj|d|tj| d||S(Ni(R9RPR$RR(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMNscC`stj|j||| S(N(R$RRO(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#QscC`stjd|||  S(Ni(R$R(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRNTscC`stj|j|||S(N(R9R:RO(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&WscC`stj| ||S(N(R$R(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyROZscC`s'tjd|tj| d|S(Nii(R$RR(RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)]scC`s*d||}|tjd|||S(Ng?(R$R(RR RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRcs(R,R-R.RReRfR!RMR#RNR&ROR)R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs(        tburr12tfisk_gencB`s;eZdZdZdZdZdZdZRS(sA Fisk continuous random variable. The Fisk distribution is also known as the log-logistic distribution. %(before_notes)s Notes ----- The probability density function for `fisk` is: .. math:: f(x, c) = c x^{-c-1} (1 + x^{-c})^{-2} for :math:`x > 0` and :math:`c > 0`. `fisk` takes ``c`` as a shape parameter for :math:`c`. `fisk` is a special case of `burr` or `burr12` with ``d=1``. %(after_notes)s See Also -------- burr %(example)s cC`stj|||dS(Ng?(RR!(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stj|||dS(Ng?(RR#(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stj|||dS(Ng?(RR)(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`stj|||dS(Ng?(RR(RR R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscC`sdtj|S(Ni(R9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs(R,R-R.R!R#R)RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRks     tfiskt cauchy_gencB`sYeZdZdZdZdZdZdZdZdZ d dZ RS( s A Cauchy continuous random variable. %(before_notes)s Notes ----- The probability density function for `cauchy` is .. math:: f(x) = \frac{1}{\pi (1 + x^2)} for a real number :math:`x`. %(after_notes)s %(example)s cC`sdtjd||S(Ng?(R9RQ(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`sddtjtj|S(Ng?g?(R9RQtarctan(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stjtj|tjdS(Ng@(R9ttanRQ(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`sddtjtj|S(Ng?g?(R9RQR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`stjtjdtj|S(Ng@(R9RRQ(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+scC`stjtjtjtjfS(N(R9Rd(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`stjdtjS(Ni(R9RPRQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRscC`s6tj|dddg\}}}|||dfS(Nii2iKi(R9t percentile(RR\Rytp25tp50tp75((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs$N( R,R-R.R!R#R)R&R+R RRRWR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs       tcauchytchi_gencB`sDeZdZdZdZdZdZdZdZRS(sA chi continuous random variable. %(before_notes)s Notes ----- The probability density function for `chi` is: .. math:: f(x, k) = \frac{1}{2^{k/2-1} \Gamma \left( k/2 \right)} x^{k-1} \exp \left( -x^2/2 \right) for :math:`x > 0` and :math:`k > 0` (degrees of freedom, denoted ``df`` in the implementation). :math:`\Gamma` is the gamma function (`scipy.special.gamma`). Special cases of `chi` are: - ``chi(1, loc, scale)`` is equivalent to `halfnorm` - ``chi(2, 0, scale)`` is equivalent to `rayleigh` - ``chi(3, 0, scale)`` is equivalent to `maxwell` `chi` takes ``df`` as a shape parameter. %(after_notes)s %(example)s cC`s5|j|j}}tjtj|d|d|S(NRR(RKRIR9R[tchi2R(RtdfRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`sYtjddtjd|tjd|}|tj|d|d|dS(Nig?g?(R9RPR$tgammalnR(RRRtl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs5cC`stjd|d|dS(Ng?i(R$tgammainc(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s!tjdtjd||S(Nig?(R9R[R$t gammaincinv(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`stjdtj|ddtj|d}|||}d|d|dd|tjtj|d}d|d|d|d d |dd|d}|tj|d}||||fS( Nig@g?g@ig?g?ii(R9R[R$RRYtpower(RRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s 576( R,R-R.RLR!RMR#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs     tchitchi2_gencB`sVeZdZdZdZdZdZdZdZdZ dZ RS( sA chi-squared continuous random variable. %(before_notes)s Notes ----- The probability density function for `chi2` is: .. math:: f(x, k) = \frac{1}{2^{k/2} \Gamma \left( k/2 \right)} x^{k/2-1} \exp \left( -x/2 \right) for :math:`x > 0` and :math:`k > 0` (degrees of freedom, denoted ``df`` in the implementation). `chi2` takes ``df`` as a shape parameter. %(after_notes)s %(example)s cC`s|jj||jS(N(RIt chisquareRK(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL*scC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!-scC`sFtj|dd||dtj|dtjd|dS(Ng@ii(R$RRR9RP(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM1scC`stj||S(N(R$tchdtr(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#4scC`stj||S(N(R$tchdtrc(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&7scC`stj||S(N(R$tchdtri(RtpR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+:scC`s|jd||S(Ng?(R+(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)=scC`sA|}d|}dtjd|}d|}||||fS(Nig@g(@(R9R[(RRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR @s   ( R,R-R.RLR!RMR#R&R+R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs       Rt cosine_gencB`s2eZdZdZdZdZdZRS(s\A cosine continuous random variable. %(before_notes)s Notes ----- The cosine distribution is an approximation to the normal distribution. The probability density function for `cosine` is: .. math:: f(x) = \frac{1}{2\pi} (1+\cos(x)) for :math:`-\pi \le x \le \pi`. %(after_notes)s %(example)s cC`sdtjdtj|S(Ng?iig?(R9RQRi(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!`scC`s#dtjtj|tj|S(Ng?ig?(R9RQRj(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#dscC`sKdtjtjddddtjdddtjtjdd fS( Ngg@g@giiZg@ii(R9RQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR gscC`stjdtjdS(Nig?(R9RPRQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRjs(R,R-R.R!R#R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRKs    tcosinet dgamma_gencB`sMeZdZdZdZdZdZdZdZdZ RS(sA double gamma continuous random variable. %(before_notes)s Notes ----- The probability density function for `dgamma` is: .. math:: f(x, a) = \frac{1}{2\Gamma(a)} |x|^{a-1} \exp(-|x|) for a real number :math:`x` and :math:`a > 0`. :math:`\Gamma` is the gamma function (`scipy.special.gamma`). `dgamma` takes ``a`` as a shape parameter for :math:`a`. %(after_notes)s %(example)s cC`s]|j|j}}|jd|}tj|d|d|}|tj|dkddS(NRRg?ii(RKRIt random_sampleRRR9R(RR/RRtutgm((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`s;t|}ddtj|||dtj| S(Ng?i(tabsR$RR9R:(RRR/tax((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!s cC`s>t|}tj|d||tjdtj|S(Ng?i(RR$RR9RPR(RRR/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs cC`s=dtj|t|}tj|dkd|d|S(Ng?i(R$RRR9R(RRR/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s=dtj|t|}tj|dkd|d|S(Ng?i(R$RRR9R(RRR/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`s>tj|dtd|d}tj|dk|| S(Niig?(R$t gammainccinvRR9R(RR(R/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)s$cC`s2||d}d|d|d|d|dfS(Ng?gg@g@((RR/Rp((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s( R,R-R.RLR!RMR#R&R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRqs      tdgammat dweibull_gencB`sMeZdZdZdZdZdZdZdZdZ RS(svA double Weibull continuous random variable. %(before_notes)s Notes ----- The probability density function for `dweibull` is given by .. math:: f(x, c) = c / 2 |x|^{c-1} \exp(-|x|^c) for a real number :math:`x` and :math:`c > 0`. `dweibull` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`s]|j|j}}|jd|}tj|d|d|}|tj|dkddS(NRRg?ii(RKRIRt weibull_minRR9R(RRRRRtw((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`s8t|}|d||dtj|| }|S(Ng@g?(RR9R:(RRRRtPx((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!s (cC`sBt|}tj|tjdtj|d|||S(Ng@g?(RR9RPR$R(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs cC`s;dtjt|| }tj|dkd||S(Ng?ii(R9R:RR(RRRtCx1((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s]dtj|dk|d|}tjtj| d|}tj|dk|| S(Ng@g?g?(R9RRRP(RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)s# cC`s%d|dtjdd||S(Niig?(R$R(RR R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscC`sdS(Ni(iNiN(RW(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s( R,R-R.RLR!RMR#R)RR (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs      tdweibullt expon_gencB`seZdZdZdZdZdZdZdZdZ dZ d Z d Z e ed d d ZRS(sAn exponential continuous random variable. %(before_notes)s Notes ----- The probability density function for `expon` is: .. math:: f(x) = \exp(-x) for :math:`x \ge 0`. %(after_notes)s A common parameterization for `expon` is in terms of the rate parameter ``lambda``, such that ``pdf = lambda * exp(-lambda * x)``. This parameterization corresponds to using ``scale = 1 / lambda``. %(example)s cC`s|jj|jS(N(RItstandard_exponentialRK(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`stj| S(N(R9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s| S(N((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`stj|  S(N(R$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`stj|  S(N(R$R(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`stj| S(N(R9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`s| S(N((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyROscC`stj| S(N(R9RP(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+scC`sdS(Ng?g@g@(g?g?g@g@((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`sdS(Ng?((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRsRSs This function uses explicit formulas for the maximum likelihood estimation of the exponential distribution parameters, so the `optimizer`, `loc` and `scale` keyword arguments are ignored. c O`sPt|dkr!tdn|jdd}|jdd}|jdd|jdd|jdd|rtd|n|dk r|dk rtd ntj|}|j}|dkr|}n0|}||krtd d |d tj n|dkr4|j |}n|}t |t |fS( NisToo many arguments.RTRUR^R_t optimizersUnknown arguments: %s.s3All parameters fixed. There is nothing to optimize.texponRvRw( Rt TypeErrortpopRWRXR9RYtminRtRcRZtfloat( RR\RyR]RTRUtdata_minR^R_((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR`s,     (R,R-R.RLR!RMR#R)R&ROR+R RRRRR`(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs           Rt exponnorm_gencB`sDeZdZdZdZdZdZdZdZRS(s'An exponentially modified Normal continuous random variable. %(before_notes)s Notes ----- The probability density function for `exponnorm` is: .. math:: f(x, K) = \frac{1}{2K} \exp\left(\frac{1}{2 K^2} - x / K \right) \text{erfc}\left(-\frac{x - 1/K}{\sqrt{2}}\right) where :math:`x` is a real number and :math:`K > 0`. It can be thought of as the sum of a standard normal random variable and an independent exponentially distributed random variable with rate ``1/K``. %(after_notes)s An alternative parameterization of this distribution (for example, in `Wikipedia `_) involves three parameters, :math:`\mu`, :math:`\lambda` and :math:`\sigma`. In the present parameterization this corresponds to having ``loc`` and ``scale`` equal to :math:`\mu` and :math:`\sigma`, respectively, and shape parameter :math:`K = 1/(\sigma\lambda)`. .. versionadded:: 0.16.0 %(example)s cC`s6|jj|j|}|jj|j}||S(N(RIRRKRJ(RtKtexpvaltgval((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLuscC`sld|}d|d||}t|tk|ftjt}d||tj|| tjdS(Ng?g?i(R RR9R:RR$terfcR[(RRRtinvKtexpargR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!zs !cC`sTd|}d|d||}|tjd|tj|| tjdS(Ng?g?i(R9RPR$RR[(RRRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs cC`sAd|}|d||}t|tj|t||S(Ng?g?(R@R9R:(RRRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#s cC`sBd|}|d||}t| tj|t||S(Ng?g?(R@R9R:(RRRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&s cC`sP||}d|}d|d|d}d|||d}||||fS(Ng?iigg@i((RRtK2topK2tskwtkrt((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s   ( R,R-R.RLR!RMR#R&R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs"    t exponnormt exponweib_gencB`s2eZdZdZdZdZdZRS(sAn exponentiated Weibull continuous random variable. %(before_notes)s Notes ----- The probability density function for `exponweib` is: .. math:: f(x, a, c) = a c (1-\exp(-x^c))^{a-1} \exp(-x^c) x^{c-1} for :math:`x > 0`, :math:`a > 0`, :math:`c > 0`. `exponweib` takes :math:`a` and :math:`c` as shape parameters. %(after_notes)s %(example)s cC`stj|j|||S(N(R9R:RM(RRR/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`sg|| }tj| }tj|tj|tj|d||tj|d|}|S(Ng?(R$RR9RPR(RRR/Rtnegxctexm1ctlogp((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs HcC`stj||  }||S(N(R$R(RRR/RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s(tj|d|  tjd|S(Ng?(R$RR9RY(RR(R/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)s(R,R-R.R!RMR#R)(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs    t exponweibt exponpow_gencB`sDeZdZdZdZdZdZdZdZRS(sAn exponential power continuous random variable. %(before_notes)s Notes ----- The probability density function for `exponpow` is: .. math:: f(x, b) = b x^{b-1} \exp(1 + x^b - \exp(x^b)) for :math:`x \ge 0`, :math:`b > 0`. Note that this is a different distribution from the exponential power distribution that is also known under the names "generalized normal" or "generalized Gaussian". `exponpow` takes ``b`` as a shape parameter for :math:`b`. %(after_notes)s References ---------- http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Exponentialpower.pdf %(example)s cC`stj|j||S(N(R9R:RM(RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`sF||}dtj|tj|d||tj|}|S(Nig?(R9RPR$RR:(RRRltxbtf((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs 8cC`stjtj||  S(N(R$R(RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stjtj|| S(N(R9R:R$R(RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`stjtj| d|S(Ng?(R$RR9RP(RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+scC`s%ttjtj|  d|S(Ng?(tpowR$R(RR(Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)s( R,R-R.R!RMR#R&R+R)(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs     texponpowtfatiguelife_gencB`sMeZdZejZdZdZdZdZ dZ dZ RS(s/A fatigue-life (Birnbaum-Saunders) continuous random variable. %(before_notes)s Notes ----- The probability density function for `fatiguelife` is: .. math:: f(x, c) = \frac{x+1}{2c\sqrt{2\pi x^3}} \exp(-\frac{(x-1)^2}{2x c^2}) for :math:`x > 0` and :math:`c > 0`. `fatiguelife` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s References ---------- .. [1] "Birnbaum-Saunders distribution", https://en.wikipedia.org/wiki/Birnbaum-Saunders_distribution %(example)s cC`sX|jj|j}d||}||}dd|d|tjd|}|S(Ng?g?ii(RIRJRKR9R[(RRtzRtx2tt((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLs  'cC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!$scC`sgtj|d|ddd||dtjd|dtjdtjdtj|S(Niig@g?i(R9RPRQ(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM)s=cC`s,td|tj|dtj|S(Ng?(R@R9R[(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#-scC`s4|tj|}d|tj|dddS(Ng?ii(R$RCR9R[(RR(Rttmp((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)0scC`s||}|dd}d|d}||d}d|d|dtj|d}d |d |d |d}||||fS( Ng@g?g@g@ii g@g?ii]gD@(R9R(RRtc2RotdenRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR 4s &( R,R-R.RReRfRLR!RMR#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s      t fatiguelifetfoldcauchy_gencB`s2eZdZdZdZdZdZRS(s[A folded Cauchy continuous random variable. %(before_notes)s Notes ----- The probability density function for `foldcauchy` is: .. math:: f(x, c) = \frac{1}{\pi (1+(x-c)^2)} + \frac{1}{\pi (1+(x+c)^2)} for :math:`x \ge 0`. `foldcauchy` takes ``c`` as a shape parameter for :math:`c`. %(example)s cC`s(ttjd|d|jd|jS(NR^RR(RRRRKRI(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLZscC`s3dtjdd||ddd||dS(Ng?ii(R9RQ(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!^scC`s-dtjtj||tj||S(Ng?(R9RQR(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#bscC`stjtjtjtjfS(N(R9RcRd(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR es(R,R-R.RLR!R#R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRFs    t foldcauchytf_gencB`sMeZdZdZdZdZdZdZdZdZ RS(sAn F continuous random variable. %(before_notes)s Notes ----- The probability density function for `f` is: .. math:: f(x, df_1, df_2) = \frac{df_2^{df_2/2} df_1^{df_1/2} x^{df_1 / 2-1}} {(df_2+df_1 x)^{(df_1+df_2)/2} B(df_1/2, df_2/2)} for :math:`x > 0`. `f` takes ``dfn`` and ``dfd`` as shape parameters. %(after_notes)s %(example)s cC`s|jj|||jS(N(RIR RK(Rtdfntdfd((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`stj|j|||S(N(R9R:RM(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`sd|}d|}|dtj||dtj||ddtj|}|||dtj|||tj|d|d8}|S(Ng?ii(R9RPR$R(RRRRR tmR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs   E?cC`stj|||S(N(R$tfdtr(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stj|||S(N(R$tfdtrc(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`stj|||S(N(R$tfdtri(RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)sc C`sd|d|}}|d|d|d|df\}}}}t|dk||fdtj} t|dk||||fd tj} t|d k||||fd tj} | tjd9} t|d k| ||fd tj} | d9} | | | | fS(Ng?g@g@g@g @icS`s||S(N((tv2tv2_2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pytsicS`s$d||||||d|S(Ni((tv1RRtv2_4((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR sicS`s)d|||tj||||S(Ni(R9R[(R!RR"tv2_6((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR sicS`sd||||S(Ni((RqR#tv2_8((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR sg@g?(R R9RcRdR[( RRRR!RRR"R#R$RoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s*.     ( R,R-R.RLR!RMR#R&R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRls      R t foldnorm_gencB`s;eZdZdZdZdZdZdZRS(sfA folded normal continuous random variable. %(before_notes)s Notes ----- The probability density function for `foldnorm` is: .. math:: f(x, c) = \sqrt{2/\pi} cosh(c x) \exp(-\frac{x^2+c^2}{2}) for :math:`c \ge 0`. `foldnorm` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`s |dkS(Ni((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _argcheckscC`st|jj|j|S(N(RRIRJRK(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`st||t||S(N(R<(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s t||t||dS(Ng?(R@(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s||}tjd|tjdtj}d||tj|tjd}|d||}d||||||}|tj|d}||ddd||}|d|d d |d|d7}||dd }||||fS( Ngg@iig?g@ig @g@(R9R:R[RQR$terfR(RRRtexpfacRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s '(&(R,R-R.R&RLR!R#R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR%s     tfoldnormtweibull_min_gencB`sVeZdZdZdZdZdZdZdZdZ dZ RS( sWeibull minimum continuous random variable. %(before_notes)s See Also -------- weibull_max Notes ----- The probability density function for `weibull_min` is: .. math:: f(x, c) = c x^{c-1} \exp(-x^c) for :math:`x > 0`, :math:`c > 0`. `weibull_min` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`s,|t||dtjt|| S(Ni(R R9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s.tj|tj|d|t||S(Ni(R9RPR$RR (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`stjt||  S(N(R$RR (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR##scC`stjt|| S(N(R9R:R (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&&scC`st|| S(N(R (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRO)scC`sttj|  d|S(Ng?(R R$R(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR),scC`stjd|d|S(Ng?(R$R(RR R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR/scC`st |tj|tdS(Ni(RR9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR2s( R,R-R.R!RMR#R&ROR)RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR*s       Rtweibull_max_gencB`sVeZdZdZdZdZdZdZdZdZ dZ RS( sWeibull maximum continuous random variable. %(before_notes)s See Also -------- weibull_min Notes ----- The probability density function for `weibull_max` is: .. math:: f(x, c) = c (-x)^{c-1} \exp(-(-x)^c) for :math:`x < 0`, :math:`c > 0`. `weibull_max` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`s.|t| |dtjt| | S(Ni(R R9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!SscC`s0tj|tj|d| t| |S(Ni(R9RPR$RR (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMWscC`stjt| | S(N(R9R:R (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#ZscC`st| | S(N(R (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRN]scC`stjt| |  S(N(R$RR (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&`scC`sttj| d| S(Ng?(R R9RP(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)cscC`sBtjd|d|}t|dr4d}nd}||S(Ng?iii(R$Rtint(RR Rtvaltsgn((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRfs  cC`st |tj|tdS(Ni(RR9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRns( R,R-R.R!RMR#RNR&R)RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+9s       t weibull_maxslThe distribution `frechet_r` is a synonym for `weibull_min`; this historical usage is deprecated because of possible confusion with the (quite different) Frechet distribution. To preserve the existing behavior of the program, use `scipy.stats.weibull_min`. For the Frechet distribution (i.e. the Type II extreme value distribution), use `scipy.stats.invweibull`.t frechet_r_gencB`seZejdddedZejdddedZejdddedZejdddedZejdddedZ ejdddedZ ejddded Z ejddded Z ejddded Z ejddded Zejddded ZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZRS(told_namet frechet_rtmessagecO`stj|||S(N(R*t__call__(RRytkwargs((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR4scO`stj|||S(N(R*tcdf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR6scO`stj|||S(N(R*tentropy(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR7scO`stj|||S(N(R*texpect(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR8scO`stj|||S(N(R*R`(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR`scO`stj|||S(N(R*t fit_loc_scale(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR9scO`stj|||S(N(R*tfreeze(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR:scO`stj|||S(N(R*tinterval(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR;scO`stj|||S(N(R*tisf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR<scO`stj|||S(N(R*tlogcdf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR=scO`stj|||S(N(R*tlogpdf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR>scO`stj|||S(N(R*tlogsf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR?scO`stj|||S(N(R*RZ(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRZscO`stj|||S(N(R*tmedian(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR@scO`stj|||S(N(R*tmoment(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRAscO`stj|||S(N(R*tnnlf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRBscO`stj|||S(N(R*tpdf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRCscO`stj|||S(N(R*tppf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRDscO`stj|||S(N(R*R(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscO`stj|||S(N(R*tsf(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyREscO`stj|||S(N(R*tstats(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRFscO`stj|||S(N(R*tstd(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRGscO`stj|||S(N(R*R(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs(R,R-R9t deprecatet_frechet_r_deprec_msgR4R6R7R8R`R9R:R;R<R=R>R?RZR@RARBRCRDRRERFRGR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR0s.!!!!!!!!!!!!!!!!!!!!!!R2slThe distribution `frechet_l` is a synonym for `weibull_max`; this historical usage is deprecated because of possible confusion with the (quite different) Frechet distribution. To preserve the existing behavior of the program, use `scipy.stats.weibull_max`. For the Frechet distribution (i.e. the Type II extreme value distribution), use `scipy.stats.invweibull`.t frechet_l_gencB`seZejdddedZejdddedZejdddedZejdddedZejdddedZ ejdddedZ ejddded Z ejddded Z ejddded Z ejddded Zejddded ZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZejdddedZRS(R1t frechet_lR3cO`stj|||S(N(R+R4(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR4scO`stj|||S(N(R+R6(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR6scO`stj|||S(N(R+R7(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR7scO`stj|||S(N(R+R8(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR8scO`stj|||S(N(R+R`(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR`scO`stj|||S(N(R+R9(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR9scO`stj|||S(N(R+R:(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR:scO`stj|||S(N(R+R;(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR;scO`stj|||S(N(R+R<(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR< scO`stj|||S(N(R+R=(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR=scO`stj|||S(N(R+R>(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR>scO`stj|||S(N(R+R?(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR?scO`stj|||S(N(R+RZ(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRZscO`stj|||S(N(R+R@(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR@scO`stj|||S(N(R+RA(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRA#scO`stj|||S(N(R+RB(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRB'scO`stj|||S(N(R+RC(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRC+scO`stj|||S(N(R+RD(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRD/scO`stj|||S(N(R+R(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR3scO`stj|||S(N(R+RE(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRE7scO`stj|||S(N(R+RF(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRF;scO`stj|||S(N(R+RG(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRG?scO`stj|||S(N(R+R(RRyR5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRCs(R,R-R9RHt_frechet_l_deprec_msgR4R6R7R8R`R9R:R;R<R=R>R?RZR@RARBRCRDRRERFRGR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRJs.!!!!!!!!!!!!!!!!!!!!!!RKtgenlogistic_gencB`s;eZdZdZdZdZdZdZRS(sA generalized logistic continuous random variable. %(before_notes)s Notes ----- The probability density function for `genlogistic` is: .. math:: f(x, c) = c \frac{\exp(-x)} {(1 + \exp(-x))^{c+1}} for :math:`x > 0`, :math:`c > 0`. `genlogistic` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!bscC`s0tj|||dtjtj| S(Ng?(R9RPR$RR:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMfscC`sdtj| | }|S(Ni(R9R:(RRRtCx((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#iscC`s%tjt|d|d }|S(Ngi(R9RPR (RR(Rtvals((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)ms!cC`sttj|}tjtjdtjd|}dtjd|dt}|tj|d}tjdddtjd|}||d }||||fS( Ng@iiig?ig.@ig@(RR$RR9RQtzetaRR(RRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR qs$%(R,R-R.R!RMR#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMKs     t genlogistict genpareto_gencB`sheZdZdZdZdZdZdZdZdZ dZ d Z d Z RS( sA generalized Pareto continuous random variable. %(before_notes)s Notes ----- The probability density function for `genpareto` is: .. math:: f(x, c) = (1 + c x)^{-1 - 1/c} defined for :math:`x \ge 0` if :math:`c \ge 0`, and for :math:`0 \le x \le -1/c` if :math:`c < 0`. `genpareto` takes ``c`` as a shape parameter for :math:`c`. For :math:`c=0`, `genpareto` reduces to the exponential distribution, `expon`: .. math:: f(x, 0) = \exp(-x) For :math:`c=-1`, `genpareto` is uniform on ``[0, 1]``: .. math:: f(x, -1) = 1 %(after_notes)s %(example)s cC`s:tj|}t|dk|fdtj|_tS(NicS`sd|S(Ng((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s(R9RYR RcRlR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&s cC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s-t||k|dk@||fd| S(NicS`stj|d|| |S(Ng?(R$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s(R (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`stj| |  S(N(R$t inv_boxcox1p(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stj| | S(N(R$t inv_boxcox(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`s-t||k|dk@||fd| S(NicS`stj|| |S(N(R$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s(R (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyROscC`stj| |  S(N(R$tboxcox1p(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`stj||  S(N(R$tboxcox(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+sc`s>dt|dk|ffdtjdS(NcS`sd}tjd|d}xGt|tj||D]*\}}||d|d||}q8Wtj||dk|d||tjS(Ngiiig?g(R9tarangetzipR$tcombRRc(R RR-Rtkitcnk((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt__munps ("ic`s |S(N((R(t_genpareto_gen__munpR (s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR si(R R$R(RR R((R]R s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs cC`sd|S(Ng?((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs( R,R-R.R&R!RMR#R&ROR)R+RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR~s#         t genparetot genexpon_gencB`s)eZdZdZdZdZRS(sA generalized exponential continuous random variable. %(before_notes)s Notes ----- The probability density function for `genexpon` is: .. math:: f(x, a, b, c) = (a + b (1 - \exp(-c x))) \exp(-a x - b x + \frac{b}{c} (1-\exp(-c x))) for :math:`x \ge 0`, :math:`a, b, c > 0`. `genexpon` takes :math:`a`, :math:`b` and :math:`c` as shape parameters. %(after_notes)s References ---------- H.K. Ryu, "An Extension of Marshall and Olkin's Bivariate Exponential Distribution", Journal of the American Statistical Association, 1993. N. Balakrishnan, "The Exponential Distribution: Theory, Methods and Applications", Asit P. Basu. %(example)s cC`sL||tj| | tj| |||tj| | |S(N(R$RR9R:(RRR/RlR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!s,cC`s2tj| |||tj| | | S(N(R$R(RRR/RlR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`sLtj||tj| | | |||tj| | |S(N(R9RPR$R(RRR/RlR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMs(R,R-R.R!R#RM(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR_s  tgenexpontgenextreme_gencB`seZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZRS(s"A generalized extreme value continuous random variable. %(before_notes)s See Also -------- gumbel_r Notes ----- For :math:`c=0`, `genextreme` is equal to `gumbel_r`. The probability density function for `genextreme` is: .. math:: f(x, c) = \begin{cases} \exp(-\exp(-x)) \exp(-x) &\text{for } c = 0\\ \exp(-(1-c x)^{1/c}) (1-c x)^{1/c-1} &\text{for } x \le 1/c, c > 0 \end{cases} Note that several sources and software packages use the opposite convention for the sign of the shape parameter :math:`c`. `genextreme` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`stj|dkdtj|ttj|_tj|dkdtj|t tj |_tjt|tjkddS(Nig?i( R9RtmaximumRRcRltminimumR/R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&% s13cC`s-t||k|dk@||fd| S(NicS`stj| ||S(N(R$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR , s(R (RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _loglogcdf* scC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!. scC`st||k|dk@||fdd}tj| }|j||}tj|}tj||dk|tj k@dtj|dk|tj kBtj | ||}tj||dk|dk@d|S(NicS`s||S(N((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR 5 sgi( R R$RRdR9R:tputmaskRcR(RRRtcxtlogex2tlogpex2tpex2R>((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM4 s.'#cC`stj|j|| S(N(R9R:Rd(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRNA scC`stj|j||S(N(R9R:RN(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#D scC`stj|j|| S(N(R$RRN(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&G scC`sFtjtj|  }t||k|dk@||fd|S(NicS`stj| | |S(N(R$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR M s(R9RPR (RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)J scC`sGtjtj|   }t||k|dk@||fd|S(NicS`stj| | |S(N(R$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR R s(R9RPR$RR (RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+O sc `sGfd}|d}|d}|d}|d}tjtdktjdd||dtjtdktjddtjtjdd dtjd d}d }tjt|kt tjtjd} tjd ktj| } tjd ktj|d|} t dk|||ffd dtj} tjt|dkdtj dt tjd| } t dk||||fddtj}tjt|dkd|d}| | | |fS(Nc`stj|dS(Ni(R$R(R (R(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR U siiiigHz>g@g@g?g+=ggc`s*tj|| |d|dS(Nig?(R9tsign(RRqRrtg3tg2gm12(tg2mg12(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR f st fillvalueg(\?i icS`s(|d|d|||||dS(Niii((RqRrRktg4Rm((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR n sgq= ףp?g(@g@g@gUUUUUUտgпg333333@( R9RRRQR$RRRRdR R[R(RRtgRqRrRkRotgam2ktepstgamkRtvtsk1Rtku1R((RRms=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR T s.    8#@<&  A   )cC`sFt|}|dkr!d}nd}tt|j|d|fS(Nig?gRy(RRRaR(RR\RpR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRt s    cC`stjd|d}d||tjtj||d|tj||ddd}tj||dk|tjS(Niig?itaxis(R9RWRR$RYRRRc(RR RRRO((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR} s / cC`std|dS(Ni(R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s(R,R-R.R&RdR!RMRNR#R&R)R+R RRRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRa s          t genextremec`sd}fd}dkr_tjd}dkrtj||dd}|Sn5dkrtjd d }nd |}tj||d d dt\}}}}|dkrtdn|dS(Ngox?c`stj|S(N(R$tdigamma(R(ty(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR  sgg?i ttolg|=ig-@g뭁,?g?txtolgdy=Ris"_digammainv: fsolve failed, y = %ri(R9R:RtnewtonRRt RuntimeError(Rzt_emRtx0tvalueRRR~((Rzs=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _digammainv s     t gamma_gencB`szeZdZdZdZdZdZdZdZdZ dZ d Z e e d d d ZRS( sIA gamma continuous random variable. %(before_notes)s See Also -------- erlang, expon Notes ----- The probability density function for `gamma` is: .. math:: f(x, a) = \frac{x^{a-1} \exp(-x)}{\Gamma(a)} for :math:`x \ge 0`, :math:`a > 0`. Here :math:`\Gamma(a)` refers to the gamma function. `gamma` takes ``a`` as a shape parameter for :math:`a`. When :math:`a` is an integer, `gamma` reduces to the Erlang distribution, and when :math:`a=1` to the exponential distribution. %(after_notes)s %(example)s cC`s|jj||jS(N(RItstandard_gammaRK(RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL scC`stj|j||S(N(R9R:RM(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s%tj|d||tj|S(Ng?(R$RR(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`stj||S(N(R$R(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`stj||S(N(R$t gammaincc(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& scC`stj||S(N(R$R(RR(R/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`s!||dtj|d|fS(Ng@g@(R9R[(RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`s&tj|d||tj|S(Ni(R$RR(RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR scC`s7ddt|d}tt|j|d|fS(Nig:0yE>iRy(RRRR(RR\R/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR sRSs When the location is fixed by using the argument `floc`, this function uses explicit formulas or solves a simpler numerical problem than the full ML optimization problem. So in that case, the `optimizer`, `loc` and `scale` arguments are ignored. c`s|jddp3|jddp3|jdd}|jdd}|jdd}|dkrtt|j|||S|dk r|dk rtdntj|}tj||krt dd|d tj n|d kr||}n|j }|dkr|dk r1|}ntj |tj |j fd } d tj d d dd} | d} | d} tj| | | dd }||} n4tj |j tj |}t|}|} ||| fS(NRRRRTRUs3All parameters fixed. There is nothing to optimize.RRvRwic`stj|tj|S(N(R9RPR$Ry(R/(R(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR ' siiii ig?tdispg333333?gffffff?(RVRWRRR`RXR9RYRRtRcRZRPR[RtbrentqR(RR\RyR]RRTRURR/RtaesttxaR R_R((Rs=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR` s8$       "/   " (R,R-R.RLR!RMR#R&R)R RRRRRR`(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s         Rt erlang_gencB`sNeZdZdZdZdZejdk rLejjde_nRS(sAn Erlang continuous random variable. %(before_notes)s See Also -------- gamma Notes ----- The Erlang distribution is a special case of the Gamma distribution, with the shape parameter `a` an integer. Note that this restriction is not enforced by `erlang`. It will, however, generate a warning the first time a non-integer value is used for the shape parameter. Refer to `gamma` for examples. cC`sWtjtj||k}tj|dk}|sStjd|ftn|S(NisUThe shape parameter of the erlang distribution has been given a non-integer value %r.(R9talltfloortwarningstwarntRuntimeWarning(RR/tallinttallpos((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&R s cC`s=tddt|d}tt|j|d|fS(Ng@g:0yE>iRy(R,RRRR(RR\R/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR^ scO`stt|j|||S(N(RRR`(RR\RyR]((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR`g ss Notes ----- The Erlang distribution is generally defined to have integer values for the shape parameter. This is not enforced by the `erlang` class. When fitting the distribution, it will generally return a non-integer value for the shape parameter. By using the keyword argument `f0=`, the fit method can be constrained to fit the data to a specific integer shape parameter. N(R,R-R.R&RR`RWR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR> s  terlangt gengamma_gencB`s_eZdZdZdZdZdZdZdZdZ dZ d Z RS( sA generalized gamma continuous random variable. %(before_notes)s Notes ----- The probability density function for `gengamma` is: .. math:: f(x, a, c) = \frac{|c| x^{c a-1} \exp(-x^c)}{\Gamma(a)} for :math:`x \ge 0`, :math:`a > 0`, and :math:`c \ne 0`. :math:`\Gamma` is the gamma function (`scipy.special.gamma`). `gengamma` takes :math:`a` and :math:`c` as shape parameters. %(after_notes)s %(example)s cC`s|dk|dk@S(Ni((RR/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& scC`stj|j|||S(N(R9R:RM(RRR/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s@tjt|tj||d|||tj|S(Ni(R9RPRR$RR(RRR/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`sG||}tj||}tj||}tj|dk||S(Ni(R$RRR9R(RRR/Rtxctval1tval2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# s cC`sG||}tj||}tj||}tj|dk||S(Ni(R$RRR9R(RRR/RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& s cC`sEtj||}tj||}tj|dk||d|S(Nig?(R$RRR9R(RR(R/RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`sEtj||}tj||}tj|dk||d|S(Nig?(R$RRR9R(RR(R/RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+ scC`stj||d|S(Ng?(R$tpoch(RR R/R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`sGtj|}|d|d||tj|tjt|S(Nig?(R$RRR9RPR(RR/RR-((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s( R,R-R.R&R!RMR#R&R)R+RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR{ s        tgengammatgenhalflogistic_gencB`s;eZdZdZdZdZdZdZRS(sA generalized half-logistic continuous random variable. %(before_notes)s Notes ----- The probability density function for `genhalflogistic` is: .. math:: f(x, c) = \frac{2 (1 - c x)^{1/(c-1)}}{[1 + (1 - c x)^{1/c}]^2} for :math:`0 \le x \le 1/c`, and :math:`c > 0`. `genhalflogistic` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`sd||_|dkS(Ng?i(Rl(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& s cC`sMd|}tjd||}||d}||}d|d|dS(Ng?ii(R9RY(RRRtlimitRttmp0ttmp2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! s   cC`s;d|}tjd||}||}d|d|S(Ng?i(R9RY(RRRRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# s  cC`s d|dd|d||S(Ng?i((RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`sdd|dtjdS(Nii(R9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s(R,R-R.R&R!R#R)RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s    tgenhalflogistict gompertz_gencB`s;eZdZdZdZdZdZdZRS(sqA Gompertz (or truncated Gumbel) continuous random variable. %(before_notes)s Notes ----- The probability density function for `gompertz` is: .. math:: f(x, c) = c \exp(x) \exp(-c (e^x-1)) for :math:`x \ge 0`, :math:`c > 0`. `gompertz` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s"tj|||tj|S(N(R9RPR$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`stj| tj| S(N(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`stjd|tj| S(Ng(R$R(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`s.dtj|tj|tjd|S(Ng?i(R9RPR:R$texpn(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s(R,R-R.R!RMR#R)RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s     tgompertzt gumbel_r_gencB`sMeZdZdZdZdZdZdZdZdZ RS(sA right-skewed Gumbel continuous random variable. %(before_notes)s See Also -------- gumbel_l, gompertz, genextreme Notes ----- The probability density function for `gumbel_r` is: .. math:: f(x) = \exp(-(x + e^{-x})) The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett distribution. It is also related to the extreme value distribution, log-Weibull and Gompertz distributions. %(after_notes)s %(example)s cC`stj|j|S(N(R9R:RM(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!5 scC`s| tj| S(N(R9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM9 scC`stjtj|  S(N(R9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#< scC`stj|  S(N(R9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRN? scC`stjtj|  S(N(R9RP(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)B scC`s:ttjtjddtjdtjdtdfS(Ng@i iig(@ig333333@(RR9RQR[R(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR E scC`stdS(Ng?(R(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRH s( R,R-R.R!RMR#RNR)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s      tgumbel_rt gumbel_l_gencB`s_eZdZdZdZdZdZdZdZdZ dZ d Z RS( sA left-skewed Gumbel continuous random variable. %(before_notes)s See Also -------- gumbel_r, gompertz, genextreme Notes ----- The probability density function for `gumbel_l` is: .. math:: f(x) = \exp(x - e^x) The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett distribution. It is also related to the extreme value distribution, log-Weibull and Gompertz distributions. %(after_notes)s %(example)s cC`stj|j|S(N(R9R:RM(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!j scC`s|tj|S(N(R9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMn scC`stjtj|  S(N(R$RR9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#q scC`stjtj|  S(N(R9RPR$R(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)t scC`stj| S(N(R9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyROw scC`stjtj| S(N(R9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&z scC`stjtj| S(N(R9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+} scC`s;t tjtjddtjdtjdtdfS(Ng@iiig(@ig333333@(RR9RQR[R(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`stdS(Ng?(R(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s( R,R-R.R!RMR#R)ROR&R+R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRP s        tgumbel_lthalfcauchy_gencB`sDeZdZdZdZdZdZdZdZRS(s A Half-Cauchy continuous random variable. %(before_notes)s Notes ----- The probability density function for `halfcauchy` is: .. math:: f(x) = \frac{2}{\pi (1 + x^2)} for :math:`x \ge 0`. %(after_notes)s %(example)s cC`sdtjd||S(Ng@g?(R9RQ(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s%tjdtjtj||S(Ng@(R9RPRQR$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`sdtjtj|S(Ng@(R9RQR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`stjtjd|S(Ni(R9RRQ(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`stjtjtjtjfS(N(R9RcRd(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`stjdtjS(Ni(R9RPRQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s( R,R-R.R!RMR#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s     t halfcauchythalflogistic_gencB`sDeZdZdZdZdZdZdZdZRS(sGA half-logistic continuous random variable. %(before_notes)s Notes ----- The probability density function for `halflogistic` is: .. math:: f(x) = \frac{ 2 e^{-x} }{ (1+e^{-x})^2 } = \frac{1}{2} \text{sech}(x/2)^2 for :math:`x \ge 0`. %(after_notes)s %(example)s cC`stj|j|S(N(R9R:RM(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s,tjd|dtjtj| S(Nig@(R9RPR$RR:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`stj|dS(Ng@(R9ttanh(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`sdtj|S(Ni(R9tarctanh(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`s|dkrdtjdS|dkr;tjtjdS|dkrOdtS|dkrndtjddSddtd d|tj|dtj|dS( Niig@ii iig.@g@(R9RPRQRR R$RRP(RR ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s    cC`sdtjdS(Ni(R9RP(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s( R,R-R.R!RMR#R)RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s     t halflogistict halfnorm_gencB`sMeZdZdZdZdZdZdZdZdZ RS(sEA half-normal continuous random variable. %(before_notes)s Notes ----- The probability density function for `halfnorm` is: .. math:: f(x) = \sqrt{2/\pi} \exp(-x^2 / 2) for :math:`x > 0`. `halfnorm` is a special case of `chi` with ``df=1``. %(after_notes)s %(example)s cC`st|jjd|jS(NR(RRIRJRK(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL scC`s*tjdtjtj| |dS(Ng@(R9R[RQR:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s$dtjdtj||dS(Ng?g@(R9RPRQ(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`st|ddS(Nig?(R@(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`stjd|dS(Nig@(R$RC(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`shtjdtjddtjtjddtjtjdddtjdtjddfS(Ng@iiig?ii(R9R[RQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR  s&cC`sdtjtjddS(Ng?g@(R9RPRQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s( R,R-R.RLR!RMR#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s      thalfnormt hypsecant_gencB`s;eZdZdZdZdZdZdZRS(sA hyperbolic secant continuous random variable. %(before_notes)s Notes ----- The probability density function for `hypsecant` is: .. math:: f(x) = \frac{1}{\pi} \text{sech}(x) for a real number :math:`x`. %(after_notes)s %(example)s cC`sdtjtj|S(Ng?(R9RQtcosh(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!2 scC`s!dtjtjtj|S(Ng@(R9RQRR:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#6 scC`s!tjtjtj|dS(Ng@(R9RPRRQ(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)9 scC`sdtjtjdddfS(Niii(R9RQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR < scC`stjdtjS(Ni(R9RPRQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR? s(R,R-R.R!R#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s     t hypsecanttgausshyper_gencB`s)eZdZdZdZdZRS(s@A Gauss hypergeometric continuous random variable. %(before_notes)s Notes ----- The probability density function for `gausshyper` is: .. math:: f(x, a, b, c, z) = C x^{a-1} (1-x)^{b-1} (1+zx)^{-c} for :math:`0 \le x \le 1`, :math:`a > 0`, :math:`b > 0`, and :math:`C = \frac{1}{B(a, b) F[2, 1](c, a; a+b; -z)}`. :math:`F[2, 1]` is the Gauss hypergeometric function `scipy.special.hyp2f1`. `gausshyper` takes :math:`a`, :math:`b`, :math:`c` and :math:`z` as shape parameters. %(after_notes)s %(example)s cC`s(|dk|dk@||k@||k@S(Ni((RR/RlRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&` scC`s|tj|tj|tj||tj||||| }d|||dd||dd|||S(Ng?(R$Rthyp2f1(RRR/RlRRtCinv((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!c sHc C`sttj|||tj||}tj||||||| }tj||||| }|||S(N(R$RR( RR R/RlRRRtnumR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRi s&%(R,R-R.R&R!R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRF s  t gausshypert invgamma_gencB`sbeZdZejZdZdZdZdZ dZ dZ ddZ d Z RS( sAn inverted gamma continuous random variable. %(before_notes)s Notes ----- The probability density function for `invgamma` is: .. math:: f(x, a) = \frac{x^{-a-1}}{\Gamma(a)} \exp(-\frac{1}{x}) for :math:`x > 0`, :math:`a > 0`. :math:`\Gamma` is the gamma function (`scipy.special.gamma`). `invgamma` takes ``a`` as a shape parameter for :math:`a`. `invgamma` is a special case of `gengamma` with ``c=-1``. %(after_notes)s %(example)s cC`stj|j||S(N(R9R:RM(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s+|d tj|tj|d|S(Nig?(R9RPR$R(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`stj|d|S(Ng?(R$R(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`sdtj||S(Ng?(R$R(RR(R/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`stj|d|S(Ng?(R$R(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& scC`sdtj||S(Ng?(R$R(RR(R/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+ stmvskcC`st|dk|fdtj}t|dk|fdtj}d \}}d|krt|dk|fdtj}nd|krt|d k|fd tj}n||||fS( NicS`s d|dS(Ng?((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR  sicS`sd|dd|dS(Ng?ig@((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR  sRicS`sdtj|d|dS(Ng@g@g@(R9R[(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR  sRicS`s dd|d|d|dS(Ng@g@g&@g@g@((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR  s(NN(R R9RcRWRd(RR/Rtm1tm2RqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s$    cC`s&||dtj|tj|S(Ng?(R$RR(RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s(R,R-R.RReRfR!RMR#R)R&R+R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs s        tinvgammat invgauss_gencB`sDeZdZejZdZdZdZdZ dZ RS(scAn inverse Gaussian continuous random variable. %(before_notes)s Notes ----- The probability density function for `invgauss` is: .. math:: f(x, \mu) = \frac{1}{\sqrt{2 \pi x^3}} \exp(-\frac{(x-\mu)^2}{2 x \mu^2}) for :math:`x > 0` and :math:`\mu > 0`. `invgauss` takes ``mu`` as a shape parameter for :math:`\mu`. %(after_notes)s When :math:`\mu` is too small, evaluating the cumulative distribution function will be inaccurate due to ``cdf(mu -> 0) = inf * 0``. NaNs are returned for :math:`\mu \le 0.0028`. %(example)s cC`s|jj|dd|jS(Ng?R(RItwaldRK(RRo((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL scC`sEdtjdtj|dtjdd||||dS(Ng?ig@g(R9R[RQR:(RRRo((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`sAdtjdtjdtj||||dd|S(Ngig?(R9RPRQ(RRRo((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM scC`sntjd|}t||||}|tjd|t| |||tjd|7}|S(Ng?(R9R[R@R:(RRRoRtC1((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# s?cC`s%||ddtj|d|fS(Ng@ii(R9R[(RRo((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s( R,R-R.RReRfRLR!RMR#R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s     tinvgausstnorminvgauss_gencB`s;eZdZejZdZdZdZdZ RS(sA Normal Inverse Gaussian continuous random variable. %(before_notes)s Notes ----- The probability density function for `norminvgauss` is: .. math:: f(x, a, b) = (a \exp(\sqrt{a^2 - b^2} + b x)) / (\pi \sqrt{1 + x^2} \, K_1(a \sqrt{1 + x^2})) where `x` is a real number, the parameter `a` is the tail heaviness and `b` is the asymmetry parameter satisfying `a > 0` and `abs(b) <= a`. :math:`K_1` is the modified Bessel function of second kind (`scipy.special.k1`). %(after_notes)s A normal inverse Gaussian random variable `Y` with parameters `a` and `b` can be expressed as a normal mean-variance mixture: `Y = b * V + sqrt(V) * X` where `X` is `norm(0,1)` and `V` is `invgauss(mu=1/sqrt(a**2 - b**2))`. This representation is used to generate random variates. References ---------- O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions on Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3), pp. 151-157, 1978. O. Barndorff-Nielsen, "Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling", Scandinavian Journal of Statistics, Vol. 24, pp. 1-13, 1997. %(example)s cC`s|dktj||k@S(Ni(R9tabsolute(RR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& scC`sytj|d|d}|tjtj|}tjd|}|tj||tj|||||S(Nii(R9R[RQR:thypotR$tk1e(RRR/RlRtfac1tsq((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s{tj|d|d}|j|j}}tjdd|d|d|}||tj|tjd|d|S(NiRoiRR(R9R[RKRIRRRa(RR/RlRRRtig((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL" s"cC`stj|d|d}||}|d|d}d||tj|}ddd|d|d|}||||fS(Niig@ii(R9R[(RR/RlRRZtvariancetskewnesstkurtosis((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR * s  "( R,R-R.RReRfR&R!RLR (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s '    t norminvgausstinvweibull_gencB`sDeZdZejZdZdZdZdZ dZ RS(uAn inverted Weibull continuous random variable. This distribution is also known as the Fréchet distribution or the type II extreme value distribution. %(before_notes)s Notes ----- The probability density function for `invweibull` is: .. math:: f(x, c) = c x^{-c-1} \exp(-x^{-c}) for :math:`x > 0`, :math:`c > 0`. `invweibull` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s References ---------- F.R.S. de Gusmao, E.M.M Ortega and G.M. Cordeiro, "The generalized inverse Weibull distribution", Stat. Papers, vol. 52, pp. 591-619, 2011. %(example)s cC`sFtj|| d}tj|| }tj| }|||S(Ng?(R9RR:(RRRtxc1txc2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!V scC`s!tj|| }tj| S(N(R9RR:(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#] scC`stjtj| d|S(Ng(R9RRP(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)a scC`stjd||S(Ni(R$R(RR R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRd scC`sdtt|tj|S(Ni(RR9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRg s( R,R-R.RReRfR!R#R)RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR6 s     t invweibullt johnsonsb_gencB`s;eZdZejZdZdZdZdZ RS(sA Johnson SB continuous random variable. %(before_notes)s See Also -------- johnsonsu Notes ----- The probability density function for `johnsonsb` is: .. math:: f(x, a, b) = \frac{b}{x(1-x)} \phi(a + b \log \frac{x}{1-x} ) for :math:`0 < x < 1` and :math:`a, b > 0`, and :math:`\phi` is the normal pdf. `johnsonsb` takes :math:`a` and :math:`b` as shape parameters. %(after_notes)s %(example)s cC`s|dk||k@S(Ni((RR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& scC`s=t||tj|d|}|d|d||S(Ng?i(R<R9RP(RRR/Rlttrm((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! s%cC`s#t||tj|d|S(Ng?(R@R9RP(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`s'ddtjd|t||S(Ng?ig(R9R:RD(RR(R/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) s( R,R-R.RReRfR&R!R#R)(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRn s     t johnsonsbt johnsonsu_gencB`s2eZdZdZdZdZdZRS(sA Johnson SU continuous random variable. %(before_notes)s See Also -------- johnsonsb Notes ----- The probability density function for `johnsonsu` is: .. math:: f(x, a, b) = \frac{b}{\sqrt{x^2 + 1}} \phi(a + b \log(x + \sqrt{x^2 + 1})) for all :math:`x, a, b > 0`, and :math:`\phi` is the normal pdf. `johnsonsu` takes :math:`a` and :math:`b` as shape parameters. %(after_notes)s %(example)s cC`s|dk||k@S(Ni((RR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& scC`sU||}t||tj|tj|d}|dtj|d|S(Nig?(R<R9RPR[(RRR/RlRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! s .cC`s0t||tj|tj||dS(Ni(R@R9RPR[(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`stjt|||S(N(R9tsinhRD(RR(R/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) s(R,R-R.R&R!R#R)(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s    t johnsonsut laplace_gencB`sDeZdZdZdZdZdZdZdZRS(s A Laplace continuous random variable. %(before_notes)s Notes ----- The probability density function for `laplace` is .. math:: f(x) = \frac{1}{2} \exp(-|x|) for a real number :math:`x`. %(after_notes)s %(example)s cC`s|jjddd|jS(NiiR(RItlaplaceRK(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL scC`sdtjt| S(Ng?(R9R:R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR! scC`s8tj|dkddtj| dtj|S(Nig?g?(R9RR:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`s8tj|dktjdd| tjd|S(Ng?ii(R9RRP(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`sdS(Niii(iiii((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`stjddS(Nii(R9RP(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s( R,R-R.RLR!R#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s     Rtlevy_gencB`s;eZdZejZdZdZdZdZ RS(sA Levy continuous random variable. %(before_notes)s See Also -------- levy_stable, levy_l Notes ----- The probability density function for `levy` is: .. math:: f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp\left(-\frac{1}{2x}\right) for :math:`x > 0`. This is the same as the Levy-stable distribution with :math:`a=1/2` and :math:`b=1`. %(after_notes)s %(example)s cC`s5dtjdtj||tjdd|S(Niii(R9R[RQR:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stjtjd|S(Ng?(R$RR9R[(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s tj|d }d||S(Nig?(R$RC(RR(R-((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`stjtjtjtjfS(N(R9RcRd(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR !s( R,R-R.RReRfR!R#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s     tlevyt levy_l_gencB`s;eZdZejZdZdZdZdZ RS(sA left-skewed Levy continuous random variable. %(before_notes)s See Also -------- levy, levy_stable Notes ----- The probability density function for `levy_l` is: .. math:: f(x) = \frac{1}{|x| \sqrt{2\pi |x|}} \exp{ \left(-\frac{1}{2|x|} \right)} for :math:`x < 0`. This is the same as the Levy-stable distribution with :math:`a=1/2` and :math:`b=-1`. %(after_notes)s %(example)s cC`sAt|}dtjdtj||tjdd|S(Niii(RR9R[RQR:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!Ds cC`s+t|}dtdtj|dS(Nii(RR@R9R[(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#Is cC`s t|dd}d||S(Ng?ig(RD(RR(R-((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)MscC`stjtjtjtjfS(N(R9RcRd(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR Qs( R,R-R.RReRfR!R#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR(s     tlevy_ltlevy_stable_gencB`seZdZdZdZedZedddZedZedZ ed Z ed Z d Z d Z d ZdZRS(sN A Levy-stable continuous random variable. %(before_notes)s See Also -------- levy, levy_l Notes ----- The distribution for `levy_stable` has characteristic function: .. math:: \varphi(t, \alpha, \beta, c, \mu) = e^{it\mu -|ct|^{\alpha}(1-i\beta \operatorname{sign}(t)\Phi(\alpha, t))} where: .. math:: \Phi = \begin{cases} \tan \left({\frac {\pi \alpha }{2}}\right)&\alpha \neq 1\\ -{\frac {2}{\pi }}\log |t|&\alpha =1 \end{cases} The probability density function for `levy_stable` is: .. math:: f(x) = \frac{1}{2\pi}\int_{-\infty}^\infty \varphi(t)e^{-ixt}\,dt where :math:`-\infty < t < \infty`. This integral does not have a known closed form. For evaluation of pdf we use either Zolotarev :math:`S_0` parameterization with integration, direct integration of standard parameterization of characteristic function or FFT of characteristic function. If set to other than None and if number of points is greater than ``levy_stable.pdf_fft_min_points_threshold`` (defaults to None) we use FFT otherwise we use one of the other methods. The default method is 'best' which uses Zolotarev's method if alpha = 1 and integration of characteristic function otherwise. The default method can be changed by setting ``levy_stable.pdf_default_method`` to either 'zolotarev', 'quadrature' or 'best'. To increase accuracy of FFT calculation one can specify ``levy_stable.pdf_fft_grid_spacing`` (defaults to 0.001) and ``pdf_fft_n_points_two_power`` (defaults to a value that covers the input range * 4). Setting ``pdf_fft_n_points_two_power`` to 16 should be sufficiently accurate in most cases at the expense of CPU time. For evaluation of cdf we use Zolatarev :math:`S_0` parameterization with integration or integral of the pdf FFT interpolated spline. The settings affecting FFT calculation are the same as for pdf calculation. Setting the threshold to ``None`` (default) will disable FFT. For cdf calculations the Zolatarev method is superior in accuracy, so FFT is disabled by default. Fitting estimate uses quantile estimation method in [MC]. MLE estimation of parameters in fit method uses this quantile estimate initially. Note that MLE doesn't always converge if using FFT for pdf calculations; so it's best that ``pdf_fft_min_points_threshold`` is left unset. .. warning:: For pdf calculations implementation of Zolatarev is unstable for values where alpha = 1 and beta != 0. In this case the quadrature method is recommended. FFT calculation is also considered experimental. For cdf calculations FFT calculation is considered experimental. Use Zolatarev's method instead (default). %(after_notes)s References ---------- .. [MC] McCulloch, J., 1986. Simple consistent estimators of stable distribution parameters. Communications in Statistics - Simulation and Computation 15, 11091136. .. [MS] Mittnik, S.T. Rachev, T. Doganoglu, D. Chenyao, 1999. Maximum likelihood estimation of stable Paretian models, Mathematical and Computer Modelling, Volume 29, Issue 10, 1999, Pages 275-293. .. [BS] Borak, S., Hardle, W., Rafal, W. 2005. 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As suggested by [MS]. iii(R9RWtfftRQ(tcfthR(tNR tdensityR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_pdf_from_cf_with_ffts  _cC`sN|dks$|dkr7|dkr7tj|||Stj|||SdS(Ng?g(Rt_pdf_single_value_zolotarevt_pdf_single_value_cf_integrate(RRgR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_pdf_single_value_bests$c`sMfdtjfdtj tjdddtjdS(Nc`stj|S(N(RR(R(RgR(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR sc`s(tjtjd||S(Ny(R9trealR:(R(RR(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR sRiii(RtquadR9RcRQ(RRgR((RgRRRs=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRsc `s0 tjtjddkr tj fdkrfdfdtj tjdddd drd Stjd d tjfd d tjdg}i}|jrRtj |j  rR|j  krR|j tjdkrR|j g|dxs Rws1Density calculations experimental for FFT method.s= Use combination of zolatarev and quadrature methods instead.ic`stj|S(N(RR(R(t_alphat_beta(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR sRR((i(R9RYtreshapetbroadcast_arraystdstacktemptyRtgetattrRRRRRWtvstacktlistRtarrayRRRtceilRPtmaxRR,RRtinterp1dRtT(RRRgRtdata_intdata_outtpdf_default_method_nametpdf_single_value_methodtfft_min_points_thresholdtfft_grid_spacingtfft_n_points_two_powertuniq_param_pairstpairt data_maskt data_subsett_xRR(t density_xRR ((RRs=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!bs>+     & 1  G   [-c`stj|jdddddf}tj|||\}}}tj|||fd}tjdt|df}t|dd}t|dd}t|dd}tj t d |ddddfD} x| D]} tj |ddddf| kd d} || } |dksTt| |krtj g| D]$\} t j| ^qajt| d|| s Rwu*FFT method is considered experimental for u!cumulative distribution function u/evaluations. 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( uR3t logistic_gencB`s_eZdZdZdZdZdZdZdZdZ dZ d Z RS( s\A logistic (or Sech-squared) continuous random variable. %(before_notes)s Notes ----- The probability density function for `logistic` is: .. math:: f(x) = \frac{\exp(-x)} {(1+\exp(-x))^2} `logistic` is a special case of `genlogistic` with ``c=1``. %(after_notes)s %(example)s cC`s|jjd|jS(NR(RItlogisticRK(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLMscC`stj|j|S(N(R9R:RM(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!PscC`s | dtjtj| S(Ng@(R$RR9R:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMTscC`s tj|S(N(R$texpit(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#WscC`s tj|S(N(R$tlogit(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)ZscC`stj| S(N(R$RT(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&]scC`stj| S(N(R$RU(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+`scC`sdtjtjdddfS(Nig@g@g@g333333?(R9RQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR cscC`sdS(Ng@((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRfs( R,R-R.RLR!RMR#R)R&R+R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR8s        RSt loggamma_gencB`s;eZdZdZdZdZdZdZRS(sA log gamma continuous random variable. %(before_notes)s Notes ----- The probability density function for `loggamma` is: .. math:: f(x, c) = \frac{\exp(c x - \exp(x))} {\Gamma(c)} for all :math:`x, c > 0`. Here, :math:`\Gamma` is the gamma function (`scipy.special.gamma`). `loggamma` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`s"tj|jj|d|jS(NR(R9RPRIRRK(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`s+tj||tj|tj|S(N(R9R:R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stj|tj|S(N(R$RR9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stjtj||S(N(R9RPR$R(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`smtj|}tjd|}tjd|tj|d}tjd|||}||||fS(Niig?i(R$Ryt polygammaR9R(RRRZRRtexcess_kurtosis((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s "(R,R-R.RLR!R#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRVns     tloggammatloglaplace_gencB`s;eZdZdZdZdZdZdZRS(s|A log-Laplace continuous random variable. %(before_notes)s Notes ----- The probability density function for `loglaplace` is: .. math:: f(x, c) = \begin{cases}\frac{c}{2} x^{ c-1} &\text{for } 0 < x < 1\\ \frac{c}{2} x^{-c-1} &\text{for } x \ge 1 \end{cases} for :math:`c > 0`. `loglaplace` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s References ---------- T.J. Kozubowski and K. Podgorski, "A log-Laplace growth rate model", The Mathematical Scientist, vol. 28, pp. 49-60, 2003. %(example)s cC`s6|d}tj|dk|| }|||dS(Ng@i(R9R(RRRtcd2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!s cC`s.tj|dkd||dd|| S(Nig?(R9R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s5tj|dkd|d|dd|d|S(Ng?g@g?ig(R9R(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s|d|d|dS(Ni((RR R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscC`stjd|dS(Ng@g?(R9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs(R,R-R.R!R#R)RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRZs     t loglaplacecC`s&t|dk||fdtj S(NicS`sCtj|d d|dtj||tjdtjS(Ni(R9RPR[RQ(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s(R R9Rc(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt_lognorm_logpdfst lognorm_gencB`seZdZejZdZdZdZdZ dZ dZ dZ dZ d Zd Zeed d d ZRS(sA lognormal continuous random variable. %(before_notes)s Notes ----- The probability density function for `lognorm` is: .. math:: f(x, s) = \frac{1}{s x \sqrt{2\pi}} \exp\left(-\frac{\log^2(x)}{2s^2}\right) for :math:`x > 0`, :math:`s > 0`. `lognorm` takes ``s`` as a shape parameter for :math:`s`. %(after_notes)s A common parametrization for a lognormal random variable ``Y`` is in terms of the mean, ``mu``, and standard deviation, ``sigma``, of the unique normally distributed random variable ``X`` such that exp(X) = Y. This parametrization corresponds to setting ``s = sigma`` and ``scale = exp(mu)``. %(example)s cC`s tj||jj|jS(N(R9R:RIRJRK(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s t||S(N(R](RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`sttj||S(N(R@R9RP(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`sttj||S(N(RBR9RP(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRNscC`stj|t|S(N(R9R:RD(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) scC`sttj||S(N(RER9RP(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& scC`sttj||S(N(RFR9RP(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyROscC`s|tj||}tj|}||d}tj|dd|}tjdddddg|}||||fS(Niiiig(R9R:R[tpolyval(RRRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s !cC`s-ddtjdtjdtj|S(Ng?ii(R9RPRQ(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRsRSs" When the location parameter is fixed by using the `floc` argument, this function uses explicit formulas for the maximum likelihood estimation of the log-normal shape and scale parameters, so the `optimizer`, `loc` and `scale` keyword arguments are ignored. c O`s|jdd}|dkr:tt|j|||S|jddpm|jddpm|jdd}|jdd}t|dkrtdnx6ddddddd d gD]}|j|dqW|rtd |n|dk r|dk rtd nt j |}t |}|d krP||}nt j |d krt dd|dt jnt j|}|dkrt j|j} |dkr|j} qt |} n2t |} t j|t j| dj} | || fS(NRTRtfstfix_sRUisToo many input arguments.R^R_RsUnknown arguments: %s.s3All parameters fixed. There is nothing to optimize.itlognormRvRwi(RVRWRR^R`RRRRXR9RYRRRtRcRPR:RZRGR[( RR\RyR]RTRRUR0tlndataR_R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR`s< $       &(R,R-R.RReRfRLR!RMR#RNR)R&ROR RRRR`(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR^s            Rbt gilbrat_gencB`sVeZdZejZdZdZdZdZ dZ dZ dZ RS(sEA Gilbrat continuous random variable. %(before_notes)s Notes ----- The probability density function for `gilbrat` is: .. math:: f(x) = \frac{1}{x \sqrt{2\pi}} \exp(-\frac{1}{2} (\log(x))^2) `gilbrat` is a special case of `lognorm` with ``s=1``. %(after_notes)s %(example)s cC`stj|jj|jS(N(R9R:RIRJRK(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLuscC`stj|j|S(N(R9R:RM(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!xscC`s t|dS(Ng?(R](RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM|scC`sttj|S(N(R@R9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stjt|S(N(R9R:RD(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`srtj}tj|}||d}tj|dd|}tjdddddg|}||||fS(Niiiig(R9teR[R_(RRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s  !cC`sdtjdtjdS(Ng?i(R9RPRQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs( R,R-R.RReRfRLR!RMR#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRd_s       tgilbratt maxwell_gencB`sDeZdZdZdZdZdZdZdZRS(sA Maxwell continuous random variable. %(before_notes)s Notes ----- A special case of a `chi` distribution, with ``df=3``, ``loc=0.0``, and given ``scale = a``, where ``a`` is the parameter used in the Mathworld description [1]_. The probability density function for `maxwell` is: .. math:: f(x) = \sqrt{2/\pi}x^2 \exp(-x^2/2) for :math:`x > 0`. %(after_notes)s References ---------- .. [1] http://mathworld.wolfram.com/MaxwellDistribution.html %(example)s cC`stjdd|jd|jS(Ng@RR(RRRKRI(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`s2tjdtj||tj| |dS(Ng@(R9R[RQR:(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stjd||dS(Ng?g@(R$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stjdtjd|S(Nig?(R9R[R$R(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`sdtjd}dtjdtjddtjtjdddtj|ddtjtjd tjd |dfS( Niiig@i i g?iii(R9RQR[(RR-((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s #cC`s tdtjdtjdS(Ng?i(RR9RPRQ(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs( R,R-R.RLR!R#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRgs     tmaxwellt mielke_gencB`s)eZdZdZdZdZRS(skA Mielke's Beta-Kappa continuous random variable. %(before_notes)s Notes ----- The probability density function for `mielke` is: .. math:: f(x, k, s) = \frac{k x^{k-1}}{(1+x^s)^{1+k/s}} for :math:`x > 0` and :math:`k, s > 0`. `mielke` takes ``k`` and ``s`` as shape parameters. %(after_notes)s %(example)s cC`s,|||dd||d|d|S(Ng?((RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s ||d|||d|S(Ng?((RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s0t||d|}t|d|d|S(Ng?(R (RR(RRtqsk((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)s(R,R-R.R!R#R)(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRis  tmielket kappa4_gencB`sMeZdZdZdZdZdZdZdZdZ RS(sy Kappa 4 parameter distribution. %(before_notes)s Notes ----- The probability density function for kappa4 is: .. math:: f(x, h, k) = (1 - k x)^{1/k - 1} (1 - h (1 - k x)^{1/k})^{1/h-1} if :math:`h` and :math:`k` are not equal to 0. If :math:`h` or :math:`k` are zero then the pdf can be simplified: h = 0 and k != 0:: kappa4.pdf(x, h, k) = (1.0 - k*x)**(1.0/k - 1.0)* exp(-(1.0 - k*x)**(1.0/k)) h != 0 and k = 0:: kappa4.pdf(x, h, k) = exp(-x)*(1.0 - h*exp(-x))**(1.0/h - 1.0) h = 0 and k = 0:: kappa4.pdf(x, h, k) = exp(-x)*exp(-exp(-x)) kappa4 takes :math:`h` and :math:`k` as shape parameters. The kappa4 distribution returns other distributions when certain :math:`h` and :math:`k` values are used. +------+-------------+----------------+------------------+ | h | k=0.0 | k=1.0 | -inf<=k<=inf | +======+=============+================+==================+ | -1.0 | Logistic | | Generalized | | | | | Logistic(1) | | | | | | | | logistic(x) | | | +------+-------------+----------------+------------------+ | 0.0 | Gumbel | Reverse | Generalized | | | | Exponential(2) | Extreme Value | | | | | | | | gumbel_r(x) | | genextreme(x, k) | +------+-------------+----------------+------------------+ | 1.0 | Exponential | Uniform | Generalized | | | | | Pareto | | | | | | | | expon(x) | uniform(x) | genpareto(x, -k) | +------+-------------+----------------+------------------+ (1) There are at least five generalized logistic distributions. Four are described here: https://en.wikipedia.org/wiki/Generalized_logistic_distribution The "fifth" one is the one kappa4 should match which currently isn't implemented in scipy: https://en.wikipedia.org/wiki/Talk:Generalized_logistic_distribution https://www.mathwave.com/help/easyfit/html/analyses/distributions/gen_logistic.html (2) This distribution is currently not in scipy. References ---------- J.C. Finney, "Optimization of a Skewed Logistic Distribution With Respect to the Kolmogorov-Smirnov Test", A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College, (August, 2004), https://digitalcommons.lsu.edu/gradschool_dissertations/3672 J.R.M. Hosking, "The four-parameter kappa distribution". IBM J. Res. Develop. 38 (3), 25 1-258 (1994). B. Kumphon, A. Kaew-Man, P. Seenoi, "A Rainfall Distribution for the Lampao Site in the Chi River Basin, Thailand", Journal of Water Resource and Protection, vol. 4, 866-869, (2012). https://doi.org/10.4236/jwarp.2012.410101 C. Winchester, "On Estimation of the Four-Parameter Kappa Distribution", A Thesis Submitted to Dalhousie University, Halifax, Nova Scotia, (March 2000). http://www.nlc-bnc.ca/obj/s4/f2/dsk2/ftp01/MQ57336.pdf %(after_notes)s %(example)s c C`sTtj|dk|dktj|dk|dktj|dk|dktj|dk|dktj|dk|dktj|dk|dkg}d}d}d}d}t|||||||g||gdtj|_d}d}t|||||||g||gdtj|_||kS( NicS`sdt|| |S(Ng?(t float_power(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRPscS`s tj|S(N(R9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRSscS`s'tjtj|}tj |(|S(N(R9RRRc(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pytf3Vs cS`sd|S(Ng?((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pytf5[stdefaultcS`sd|S(Ng?((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRcscS`s&tjtj|}tj|(|S(N(R9RRRc(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRfs (R9t logical_andR RdR/Rl(RRRtcondlistRRRnRo((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&Hs*!        cC`stj|j|||S(N(R9R:RM(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!qsc C`stj|dk|dktj|dk|dktj|dk|dktj|dk|dkg}d}d}d}d}t|||||g|||gdtjS(NicS`sJtjd|d| |tjd|d| d||d|S(spdf = (1.0 - k*x)**(1.0/k - 1.0)*( 1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h-1.0) logpdf = ... g?(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR|scS`s1tjd|d| |d||d|S(s~pdf = (1.0 - k*x)**(1.0/k - 1.0)*np.exp(-( 1.0 - k*x)**(1.0/k)) logpdf = ... g?(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscS`s,| tjd|d| tj| S(s]pdf = np.exp(-x)*(1.0 - h*np.exp(-x))**(1.0/h - 1.0) logpdf = ... g?(R$RR9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscS`s| tj| S(sDpdf = np.exp(-x-np.exp(-x)) logpdf = ... (R9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRnsRp(R9RqR Rd( RRRRRrRRRRn((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMvs!    cC`stj|j|||S(N(R9R:RN(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#sc C`stj|dk|dktj|dk|dktj|dk|dktj|dk|dkg}d}d}d}d}t|||||g|||gdtjS(NicS`s*d|tj| d||d|S(sVcdf = (1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h) logcdf = ... g?(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscS`sd||d| S(sLcdf = np.exp(-(1.0 - k*x)**(1.0/k)) logcdf = ... g?((RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscS`s$d|tj| tj| S(sLcdf = (1.0 - h*np.exp(-x))**(1.0/h) logcdf = ... g?(R$RR9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscS`stj|  S(sBcdf = np.exp(-np.exp(-x)) logcdf = ... (R9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRnsRp(R9RqR Rd( RRRRRrRRRRn((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRNs!    c C`stj|dk|dktj|dk|dktj|dk|dktj|dk|dkg}d}d}d}d}t|||||g|||gdtjS(NicS`s d|dd||||S(Ng?((R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscS`sd|dtj| |S(Ng?(R9RP(R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscS`s tj||  tj|S(s,ppf = -np.log((1.0 - (q**h))/h) (R$RR9RP(R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRscS`stjtj|  S(N(R9RP(R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRnsRp(R9RqR Rd( RR(RRRrRRRRn((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)s!    cC`s|dkr!|dkr!d}nT|dkrP|dkrPtd||}n%|dkrotd|}nd}gtddD]!}||krdntj^q}|S(Niigi(R,trangeRWR9Rd(RRRtmaxrtrtoutputs((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s  7( R,R-R.R&R!RMR#RNR)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRlsX )  &  # tkappa4t kappa3_gencB`s;eZdZdZdZdZdZdZRS(s<Kappa 3 parameter distribution. %(before_notes)s Notes ----- The probability density function for `kappa3` is: .. math:: f(x, a) = a (a + x^a)^{-(a + 1)/a} for :math:`x > 0` and :math:`a > 0`. `kappa3` takes ``a`` as a shape parameter for :math:`a`. References ---------- P.W. Mielke and E.S. Johnson, "Three-Parameter Kappa Distribution Maximum Likelihood and Likelihood Ratio Tests", Methods in Weather Research, 701-707, (September, 1973), https://doi.org/10.1175/1520-0493(1973)101<0701:TKDMLE>2.3.CO;2 B. Kumphon, "Maximum Entropy and Maximum Likelihood Estimation for the Three-Parameter Kappa Distribution", Open Journal of Statistics, vol 2, 415-419 (2012), https://doi.org/10.4236/ojs.2012.24050 %(after_notes)s %(example)s cC`s |dkS(Ni((RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR& scC`s||||d|dS(Ngi((RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s||||d|S(Ng((RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s||| dd|S(Ng?((RR(R/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s<gtddD]!}||kr(dntj^q}|S(Nii(RsRWR9Rd(RR/tiRv((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s7(R,R-R.R&R!R#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRxs      tkappa3t moyal_gencB`sMeZdZdZdZdZdZdZdZdZ RS(sA Moyal continuous random variable. %(before_notes)s Notes ----- The probability density function for `moyal` is: .. math:: f(x) = \exp(-(x + \exp(-x))/2) / \sqrt{2\pi} for a real number :math:`x`. %(after_notes)s This distribution has utility in high-energy physics and radiation detection. It describes the energy loss of a charged relativistic particle due to ionization of the medium [1]_. It also provides an approximation for the Landau distribution. For an in depth description see [2]_. For additional description, see [3]_. References ---------- .. [1] J.E. Moyal, "XXX. Theory of ionization fluctuations", The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol 46, 263-280, (1955). :doi:`10.1080/14786440308521076` (gated) .. [2] G. Cordeiro et al., "The beta Moyal: a useful skew distribution", International Journal of Research and Reviews in Applied Sciences, vol 10, 171-192, (2012). http://www.arpapress.com/Volumes/Vol10Issue2/IJRRAS_10_2_02.pdf .. [3] C. Walck, "Handbook on Statistical Distributions for Experimentalists; International Report SUF-PFY/96-01", Chapter 26, University of Stockholm: Stockholm, Sweden, (2007). http://www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf .. versionadded:: 1.1.0 %(example)s c C`sE|j|j}}tjddddd|d|}tj| S(NR/g?R_iRR(RKRIRRR9RP(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLLs$cC`s3tjd|tj| tjdtjS(Ngi(R9R:R[RQ(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!QscC`s'tjtjd|tjdS(Ngi(R$RR9R:R[(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#TscC`s'tjtjd|tjdS(Ngi(R$R'R9R:R[(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&WscC`stjdtj|d S(Ni(R9RPR$terfcinv(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)ZscC`shtjdtj}tjdd}dtjdtjdtjd}d}||||fS(Niiig@(R9RPt euler_gammaRQR[R$RP(RRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR ]s +cC`si|dkr tjdtjS|dkrStjddtjdtjdS|dkrdtjdtjdtj}tjdtjd}dtjd}|||S|dkrXd tjdtjdtj}dtjdtjdtjd}tjdtjd }d tjd d }||||S|j|SdS( Ng?ig@g@g?iig@iii8(R9RPR}RQR$RPt_mom1_sc(RR ttmp1Rttmp3ttmp4((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRds   ' %  ')( R,R-R.RLR!R#R&R)R R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR{!s*      tmoyalt nakagami_gencB`s2eZdZdZdZdZdZRS(s}A Nakagami continuous random variable. %(before_notes)s Notes ----- The probability density function for `nakagami` is: .. math:: f(x, \nu) = \frac{2 \nu^\nu}{\Gamma(\nu)} x^{2\nu-1} \exp(-\nu x^2) for :math:`x > 0`, :math:`\nu > 0`. `nakagami` takes ``nu`` as a shape parameter for :math:`\nu`. %(after_notes)s %(example)s cC`s?d||tj||d|dtj| ||S(Nig?(R$RR9R:(RRtnu((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stj||||S(N(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s!tjd|tj||S(Ng?(R9R[R$R(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`stj|dtj|tj|}d||}|dd||d|tj|d}d|d|d|d |d d |d}|||d}||||fS( Ng?g?iig@g?iii(R$RR9R[R(RRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s -.2(R,R-R.R!R#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR}s    tnakagamitncx2_gencB`sDeZdZdZdZdZdZdZdZRS(sA non-central chi-squared continuous random variable. %(before_notes)s Notes ----- The probability density function for `ncx2` is: .. math:: f(x, k, \lambda) = \frac{1}{2} \exp(-(\lambda+x)/2) (x/\lambda)^{(k-2)/4} I_{(k-2)/2}(\sqrt{\lambda x}) for :math:`x > 0` and :math:`k, \lambda > 0`. :math:`k` specifies the degrees of freedom (denoted ``df`` in the implementation) and :math:`\lambda` is the non-centrality parameter (denoted ``nc`` in the implementation). :math:`I_\nu` denotes the modified Bessel function of first order of degree :math:`\nu` (`scipy.special.iv`). `ncx2` takes ``df`` and ``nc`` as shape parameters. %(after_notes)s %(example)s cC`s|jj|||jS(N(RItnoncentral_chisquareRK(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`st|||S(N(R(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`st|||S(N(R(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`st|||S(N(R(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stj|||S(N(R$tchndtrix(RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`sS|d|}||d|tjd|||dd|d||dfS(Ng@iig?g(@(R9R[(RRRR-((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s ( R,R-R.RLRMR!R#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs     tncx2tncf_gencB`sDeZdZdZdZdZdZdZdZRS(sA non-central F distribution continuous random variable. %(before_notes)s Notes ----- The probability density function for `ncf` is: .. math:: f(x, n_1, n_2, \lambda) = \exp(\frac{\lambda}{2} + \lambda n_1 \frac{x}{2(n_1 x+n_2)}) n_1^{n_1/2} n_2^{n_2/2} x^{n_1/2 - 1} \\ (n_2+n_1 x)^{-(n_1+n_2)/2} \gamma(n_1/2) \gamma(1+n_2/2) \\ \frac{L^{\frac{v_1}{2}-1}_{v_2/2} (-\lambda v_1 \frac{x}{2(v_1 x+v_2)})} {B(v_1/2, v_2/2) \gamma(\frac{v_1+v_2}{2})} for :math:`n_1 > 1`, :math:`n_2, \lambda > 0`. Here :math:`n_1` is the degrees of freedom in the numerator, :math:`n_2` the degrees of freedom in the denominator, :math:`\lambda` the non-centrality parameter, :math:`\gamma` is the logarithm of the Gamma function, :math:`L_n^k` is a generalized Laguerre polynomial and :math:`B` is the beta function. `ncf` takes ``df1``, ``df2`` and ``nc`` as shape parameters. %(after_notes)s %(example)s cC`s|jj||||jS(N(RIt noncentral_fRK(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLsc C`s1||}}| d|||d|||tj|dtjd|d}|tj||d8}tj|}|||d||d||dd9}|||||| d9}|tj| ||d||||d|dd9}|tj|d|d}dS(Nig@i(R$RR9R:tassoc_laguerreR( RRRRRtn1tn2ttermR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _pdf_skips M.>cC`stj||||S(N(R$tncfdtr(RRRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stj||||S(N(R$tncfdtri(RR(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s|d||}tj|d|tjd||tj|d}|tj| d|9}|tj|d|d|d|9}|S(Ng?g?g@(R$RR9R:thyp1f1(RR RRRR-R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs =)cC`stj|dktj||dd|d|}tj|dktjd|d|d||dd|||d|dd|d}||ddfS(Nig@ig?ig@(R9RRcRW(RRRRRoRp((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR $s 63( R,R-R.RLRR#R)RR (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs      tncftt_gencB`s_eZdZdZdZdZdZdZdZdZ dZ d Z RS( s3A Student's t continuous random variable. %(before_notes)s Notes ----- The probability density function for `t` is: .. math:: f(x, \nu) = \frac{\Gamma((\nu+1)/2)} {\sqrt{\pi \nu} \Gamma(\nu)} (1+x^2/\nu)^{-(\nu+1)/2} where :math:`x` is a real number and the degrees of freedom parameter :math:`\nu` (denoted ``df`` in the implementation) satisfies :math:`\nu > 0`. :math:`\Gamma` is the gamma function (`scipy.special.gamma`). %(after_notes)s %(example)s cC`s |dkS(Ni((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&HscC`s|jj|d|jS(NR(RIt standard_tRK(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLKscC`s~tj|d}tjtj|ddtj|d}|tj|tjd|d||dd}|S(Ng?ii(R9RYR:R$RR[RQ(RRRRuR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!Ns16cC`sy|d}tj|ddtj|d}|dtj|tj|ddtjd|d|8}|S(Ng?iig?(R$RR9RPRQ(RRRRuR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMWs (CcC`stj||S(N(R$tstdtr(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#]scC`stj|| S(N(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&`scC`stj||S(N(R$tstdtrit(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)cscC`stj|| S(N(R$R(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+fscC`stj|dkdtj}t|dk|fdtj}tj|dktj|}tj|dkdtj}t|dk|fdtj}tj|dktj|}||||fS(NigicS`s ||dS(Ng@((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR lsiicS`s d|dS(Ng@g@((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR qs(R9RRcR Rd(RRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR is  ( R,R-R.R&RLR!RMR#R&R)R+R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR/s       Rtnct_gencB`sGeZdZdZdZdZdZdZddZRS(sA non-central Student's t continuous random variable. %(before_notes)s Notes ----- If :math:`Y` is a standard normal random variable and :math:`V` is an independent chi-square random variable (`chi2`) with :math:`k` degrees of freedom, then .. math:: X = \frac{Y + c}{\sqrt{V/k}} has a non-central Student's t distribution on the real line. The degrees of freedom parameter :math:`k` (denoted ``df`` in the implementation) satisfies :math:`k > 0` and the noncentrality parameter :math:`c` (denoted ``nct`` in the implementation) is a real number. %(after_notes)s %(example)s cC`s|dk||k@S(Ni((RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`sj|j|j}}tjd|d|d|}tj|d|d|}|tj|tj|S(NR^RR(RKRIRaRRR9R[(RRRRRR R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLsc C`s~|d}|d}||}|||}||}|dtj|tj|d}||tjd||d|dtj|tj|d8}tj|} |d|} tjd||tj|ddd| }|tj|tj|dd}tj|ddd| } | tjtj|tj|dd} | || 9} | S(Ng?g@iig?g?( R9RPR$RR:R[RRYR( RRRRR RRRttrm1RtvalFttrm2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!s    (I2(1cC`stj|||S(N(R$tnctdtr(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stj|||S(N(R$tnctdtrit(RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)sRcC`ssd\}}}}tj|ddtj|d}tj|d|} ||d} | | | } tj|dk|| tj}tj|dk| ||| tj}d|krX|dd||d|dd| | } d||d|d} | ||| | |}tj|dk|tj|d tj}nd |krc|||d|d }|| | d|d ||d|d8}|d| d 8}||d | | |d|d}|d||d9}d|||d|d }||d ||d|}tj|d k||ddtj}n||||fS(Ng@g?iiRg@g@ig?Rg@g@ig?g@(NNNN( RWR$RR9R[RRcRRd(RRRRRoRpRqRrtgfactc11tc20tc22tc33ttc31ttmu3tc44tc42tc40tmu4((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s,("* .1 .&-( R,R-R.R&RLR!R#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRzs     tnctt pareto_gencB`sGeZdZdZdZdZdZddZdZRS(sLA Pareto continuous random variable. %(before_notes)s Notes ----- The probability density function for `pareto` is: .. math:: f(x, b) = \frac{b}{x^{b+1}} for :math:`x \ge 1`, :math:`b > 0`. `pareto` takes ``b`` as a shape parameter for :math:`b`. %(after_notes)s %(example)s cC`s||| dS(Ni((RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s d|| S(Ni((RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`std|d|S(Nig(R (RR(Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s || S(N((RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&sRc C`s(d\}}}}d|krx|dk}tj||}ttj|dtj}tj||||dnd|kr|dk}tj||}ttj|dtj}tj||||d|ddnd|kr||d k}tj||}ttj|dtj}d|dtj|d|d tj|} tj||| nd |kr|d k}tj||}ttj|dtj}d tj ddddg|tj ddddg|} tj||| n||||fS(NRiRg?Rtig@Rig@Rig@iigg(@g(NNNN( RWR9textractRRRctplaceRdR[R_( RRlRRoRpRqRrtmasktbtRO((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s2    *  4  cC`sdd|tj|S(Nig?(R9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs( R,R-R.R!R#R)R&R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs     tparetot lomax_gencB`sVeZdZdZdZdZdZdZdZdZ dZ RS( sA Lomax (Pareto of the second kind) continuous random variable. %(before_notes)s Notes ----- The probability density function for `lomax` is: .. math:: f(x, c) = \frac{c}{(1+x)^{c+1}} for :math:`x \ge 0`, :math:`c > 0`. `lomax` takes ``c`` as a shape parameter for :math:`c`. `lomax` is a special case of `pareto` with ``loc=-1.0``. %(after_notes)s %(example)s cC`s|dd||dS(Ng?((RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!5scC`s"tj||dtj|S(Ni(R9RPR$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM9scC`stj| tj| S(N(R$RR(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#<scC`stj| tj|S(N(R9R:R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&?scC`s| tj|S(N(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyROBscC`stjtj|  |S(N(R$RR(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)EscC`s7tj|dddd\}}}}||||fS(NR^gRR(RRF(RRRoRpRqRr((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR Hs'cC`sdd|tj|S(Nig?(R9RP(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRLs( R,R-R.R!RMR#R&ROR)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs       tlomaxt pearson3_gencB`sVeZdZdZdZdZdZdZdZdZ dZ RS( sjA pearson type III continuous random variable. %(before_notes)s Notes ----- The probability density function for `pearson3` is: .. math:: f(x, skew) = \frac{|\beta|}{\Gamma(\alpha)} (\beta (x - \zeta))^{\alpha - 1} \exp(-\beta (x - \zeta)) where: .. math:: \beta = \frac{2}{skew stddev} \alpha = (stddev \beta)^2 \zeta = loc - \frac{\alpha}{\beta} :math:`\Gamma` is the gamma function (`scipy.special.gamma`). `pearson3` takes ``skew`` as a shape parameter for :math:`skew`. %(after_notes)s %(example)s References ---------- R.W. Vogel and D.E. McMartin, "Probability Plot Goodness-of-Fit and Skewness Estimation Procedures for the Pearson Type 3 Distribution", Water Resources Research, Vol.27, 3149-3158 (1991). L.R. Salvosa, "Tables of Pearson's Type III Function", Ann. Math. Statist., Vol.1, 191-198 (1930). "Using Modern Computing Tools to Fit the Pearson Type III Distribution to Aviation Loads Data", Office of Aviation Research (2003). c C`sd}d}d}tjdg||\}}}|j}tj||k}|}d|||} || d} || | } | ||| } ||| ||| | | fS(Ngg?g>g@i(R9RtcopyR( RRtskewR^R_tnorm2pearson_transitiontansRtinvmaskRRgRPttransx((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _preprocess~s! cC`stjtj|dtS(Ntdtype(R9tonesRtbool(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&sc C`s~|jdg|\}}}}}}}}|||}||d}d|dtj|}d|} |||| fS(Niig@g?g@(RR9Rj( RRt_RRgRPRRtRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s - cC`sXtj|j||}|jdkrAtj|r=dS|Sd|tj|<|S(Nig(R9R:RMtndimR(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!sc C`st|j||\}}}}}}}} tjt|||| 0`. `powerlaw` takes ``a`` as a shape parameter for :math:`a`. %(after_notes)s `powerlaw` is a special case of `beta` with ``b=1``. %(example)s cC`s|||dS(Ng?((RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s!tj|tj|d|S(Ni(R9RPR$R(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`s ||dS(Ng?((RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s|tj|S(N(R9RP(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRNscC`st|d|S(Ng?(R (RR(R/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR) sc C`s||d||d|ddd|d|dtj|d|dtjddd dg|||d|d fS( Ng?g@igg@iiiii(R9R[R_(RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s (cC`sdd|tj|S(Nig?(R9RP(RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs( R,R-R.R!RMR#RNR)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs      tpowerlawtpowerlognorm_gencB`s2eZdZejZdZdZdZRS(sA power log-normal continuous random variable. %(before_notes)s Notes ----- The probability density function for `powerlognorm` is: .. math:: f(x, c, s) = \frac{c}{x s} \phi(\log(x)/s) (\Phi(-\log(x)/s))^{c-1} where :math:`\phi` is the normal pdf, and :math:`\Phi` is the normal cdf, and :math:`x > 0`, :math:`s, c > 0`. `powerlognorm` takes :math:`c` and :math:`s` as shape parameters. %(after_notes)s %(example)s cC`sL|||ttj||tttj| ||ddS(Ng?(R<R9RPR R@(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!5s"cC`s)dtttj| ||dS(Ng?(R R@R9RP(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#;scC`s)tj| ttd|d|S(Ng?(R9R:RDR (RR(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)>s( R,R-R.RReRfR!R#R)(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs    t powerlognormt powernorm_gencB`s2eZdZdZdZdZdZRS(sA power normal continuous random variable. %(before_notes)s Notes ----- The probability density function for `powernorm` is: .. math:: f(x, c) = c \phi(x) (\Phi(-x))^{c-1} where :math:`\phi` is the normal pdf, and :math:`\Phi` is the normal cdf, and :math:`x > 0`, :math:`c > 0`. `powernorm` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`s!|t|t| |dS(Ng?(R<R@(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!\scC`s*tj|t||dt| S(Ni(R9RPR>RB(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM`scC`sdt| |dS(Ng?(R@(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#cscC`sttd|d| S(Ng?(RDR (RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)fs(R,R-R.R!RMR#R)(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyREs    t powernormt rdist_gencB`s)eZdZdZdZdZRS(sDAn R-distributed continuous random variable. %(before_notes)s Notes ----- The probability density function for `rdist` is: .. math:: f(x, c) = \frac{(1-x^2)^{c/2-1}}{B(1/2, c/2)} for :math:`-1 \le x \le 1`, :math:`c > 0`. `rdist` takes ``c`` as a shape parameter for :math:`c`. This distribution includes the following distribution kernels as special cases:: c = 2: uniform c = 4: Epanechnikov (parabolic) c = 6: quartic (biweight) c = 8: triweight %(after_notes)s %(example)s cC`s4tjd|d|ddtjd|dS(Ng?ig@ig?(R9RR$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`su|tjd|d}d|tjdd|dd|d}tjtj|rqtj|||S|S(Ng?g@ig?i(R$RRR9RRRR#(RRRtterm1R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#s ,cC`sBd|dtj|dd|d}|tjd|dS(Niig?g@g?(R$R(RR Rt numerator((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs*(R,R-R.R!R#R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRms  gtrdistt rayleigh_gencB`sqeZdZejZdZdZdZdZ dZ dZ dZ dZ d Zd ZRS( s7A Rayleigh continuous random variable. %(before_notes)s Notes ----- The probability density function for `rayleigh` is: .. math:: f(x) = x \exp(-x^2/2) for :math:`x \ge 0`. `rayleigh` is a special case of `chi` with ``df=2``. %(after_notes)s %(example)s cC`stjdd|jd|jS(NiRR(RRRKRI(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`stj|j|S(N(R9R:RM(RRu((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stj|d||S(Ng?(R9RP(RRu((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`stjd|d S(Ngi(R$R(RRu((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stjdtj| S(Ni(R9R[R$R(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`stj|j|S(N(R9R:RO(RRu((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`s d||S(Ng((RRu((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyROscC`stjdtj|S(Ni(R9R[RP(RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+scC`skdtj}tjtjd|ddtjdtjtj|ddtj|d|dfS(Niiig?ii(R9RQR[(RR-((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s  &cC`stdddtjdS(Ng@ig?i(RR9RP(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs(R,R-R.RReRfRLR!RMR#R)R&ROR+R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs          trayleightreciprocal_gencB`sMeZdZdZdZdZdZdZdZdZ RS(slA reciprocal continuous random variable. %(before_notes)s Notes ----- The probability density function for `reciprocal` is: .. math:: f(x, a, b) = \frac{1}{x \log(b/a)} for :math:`a \le x \le b`, :math:`b > a > 0`. `reciprocal` takes :math:`a` and :math:`b` as shape parameters. %(after_notes)s %(example)s cC`s@||_||_tj|d||_|dk||k@S(Ng?i(R/RlR9RPR(RR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&s  cC`sd||jS(Ng?(R(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stj| tj|jS(N(R9RPR(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`s!tj|tj||jS(N(R9RPR(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s|t|d||S(Ng?(R (RR(R/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s1d|j|t|d|t|d|S(Ng?(RR (RR R/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`s/dtj||tjtj||S(Ng?(R9RP(RR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s( R,R-R.R&R!RMR#R)RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs      t reciprocaltrice_gencB`sDeZdZdZdZdZdZdZdZRS(sA Rice continuous random variable. %(before_notes)s Notes ----- The probability density function for `rice` is: .. math:: f(x, b) = x \exp(- \frac{x^2 + b^2}{2}) I_0(x b) for :math:`x > 0`, :math:`b > 0`. :math:`I_0` is the modified Bessel function of order zero (`scipy.special.i0`). `rice` takes ``b`` as a shape parameter for :math:`b`. %(after_notes)s The Rice distribution describes the length, :math:`r`, of a 2-D vector with components :math:`(U+u, V+v)`, where :math:`U, V` are constant, :math:`u, v` are independent Gaussian random variables with standard deviation :math:`s`. Let :math:`R = \sqrt{U^2 + V^2}`. Then the pdf of :math:`r` is ``rice.pdf(x, R/s, scale=s)``. %(example)s cC`s |dkS(Ni((RRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&0scC`sJ|tjd|jjdd|j}tj||jddS(NiRRwi(i(R9R[RIRJRKR(RRlR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL3scC`s%tjtj|dtj|S(Ni(R$tchndtrR9tsquare(RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#9scC`s%tjtj|dtj|S(Ni(R9R[R$RR(RR(Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)<scC`s3|tj|| ||dtj||S(Ng@(R9R:R$ti0e(RRRl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!?scC`sX|d}d|}||d}d|tj| tj|tj|d|S(Ng@i(R9R:R$RR(RR Rltnd2Rtb2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRHs   "( R,R-R.R&RLR#R)R!R(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs     tricetrecipinvgauss_gencB`s2eZdZdZdZdZdZRS(sA reciprocal inverse Gaussian continuous random variable. %(before_notes)s Notes ----- The probability density function for `recipinvgauss` is: .. math:: f(x, \mu) = \frac{1}{\sqrt{2\pi x}} \exp\left(\frac{-(1-\mu x)^2}{2\mu^2x}\right) for :math:`x \ge 0`. `recipinvgauss` takes ``mu`` as a shape parameter for :math:`\mu`. %(after_notes)s %(example)s cC`sFdtjdtj|tjd||d d||dS(Ng?iig@(R9R[RQR:(RRRo((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!lscC`s=d||d d||ddtjdtj|S(Nig@ig?(R9RPRQ(RRRo((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMqscC`sad||}d||}dtj|}dt||tjd|t| |S(Ng?g@(R9R[R@R:(RRRoRRtisqx((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#tscC`s d|jj|dd|jS(Ng?R(RIRRK(RRo((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLzs(R,R-R.R!RMR#RL(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRTs    t recipinvgausstsemicircular_gencB`s2eZdZdZdZdZdZRS(sA semicircular continuous random variable. %(before_notes)s Notes ----- The probability density function for `semicircular` is: .. math:: f(x) = \frac{2}{\pi} \sqrt{1-x^2} for :math:`-1 \le x \le 1`. %(after_notes)s %(example)s cC`s dtjtjd||S(Ng@i(R9RQR[(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s5ddtj|tjd||tj|S(Ng?g?i(R9RQR[Rk(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`sdS(Nig?g(ig?ig((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR scC`sdS(NgzCϑ?((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs(R,R-R.R!R#R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs    t semicirculart skew_norm_gencB`sGeZdZdZdZdZdZdZddZRS(sA skew-normal random variable. %(before_notes)s Notes ----- The pdf is:: skewnorm.pdf(x, a) = 2 * norm.pdf(x) * norm.cdf(a*x) `skewnorm` takes a real number :math:`a` as a skewness parameter When ``a = 0`` the distribution is identical to a normal distribution (`norm`). `rvs` implements the method of [1]_. %(after_notes)s %(example)s References ---------- .. [1] A. Azzalini and A. Capitanio (1999). Statistical applications of the multivariate skew-normal distribution. J. Roy. Statist. Soc., B 61, 579-602. http://azzalini.stat.unipd.it/SN/faq-r.html cC`s tj|S(N(R9tisfinite(RR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`sdt|t||S(Ng@(R<R@(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scG`s|dkr4tj|j|j|d|d}nQtj|j|jdd|d}tj|jd|d|d}||}|dkrd}n|S(NiRyig?(RRR!R/(RRRyR6tt1tt2((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _cdf_singles (%"   cC`s|j| | S(N(R#(RRR/((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`s|jjd|j}|jjd|j}|tjd|d}|||tjd|d}tj|dk|| S(NRiii(RItnormalRKR9R[R(RR/tu0RtRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLs #RcC`sddddg}tjdtj|tjd|d}d|krZ||dR(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`st||j|jS(N(R@RR(RRR/Rl((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`sZtj|jdkt||j|jd|t||j|jd|}|S(Nig?( R9RR/RGRRRDRR(RR(R/RlRD((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)s%c C`sv|j|j}}||}t|t|}}|||}d|||||||} || ddfS(Ni(RRR<RW( RR/RltnAtnBRtpAtpBRoRp((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s  "( R,R-R.R&R!RMR#R)R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs    t truncnormttukeylambda_gencB`sDeZdZdZdZdZdZdZdZRS(s*A Tukey-Lamdba continuous random variable. %(before_notes)s Notes ----- A flexible distribution, able to represent and interpolate between the following distributions: - Cauchy (:math:`lambda = -1`) - logistic (:math:`lambda = 0`) - approx Normal (:math:`lambda = 0.14`) - uniform from -1 to 1 (:math:`lambda = 1`) `tukeylambda` takes a real number :math:`lambda` (denoted ``lam`` in the implementation) as a shape parameter. %(after_notes)s %(example)s cC`stjtj|dtS(NR(R9RRR(Rtlam((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`stjtj||}||dtjd||d}dtj|}tj|dkt|dtj|kB|dS(Ng?iig(R9RYR$ttklmbdaRR(RRRtFxR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!s'cC`stj||S(N(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR# scC`s!tj||tj| |S(N(R$RVRU(RR(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`sdt|dt|fS(Ni(t_tlvart_tlkurt(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR sc`s&fd}tj|dddS(Nc`s/tjt|dtd|dS(Ni(R9RPR (R(R(s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pytintegsii(RR(RRR((Rs=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs( R,R-R.R&R!R#R)R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs     t tukeylambdatFitUniformFixedScaleDataErrorcB`seZdZRS(cC`sd||ff|_dS(NsInvalid values in `data`. Maximum likelihood estimation with the uniform distribution and fixed scale requires that data.ptp() <= fscale, but data.ptp() = %r and fscale = %r.(Ry(RtptpRU((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRzs(R,R-Rz(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRst uniform_gencB`sMeZdZdZdZdZdZdZdZdZ RS(s A uniform continuous random variable. In the standard form, the distribution is uniform on ``[0, 1]``. Using the parameters ``loc`` and ``scale``, one obtains the uniform distribution on ``[loc, loc + scale]``. %(before_notes)s %(example)s cC`s|jjdd|jS(Ngg?(RIRRK(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL4scC`sd||kS(Ng?((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!7scC`s|S(N((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#:scC`s|S(N((RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)=scC`sddddfS(Ng?g?i ig333333gUUUUUU?((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR @scC`sdS(Ng((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRCsc O`st|dkr!tdn|jdd}|jdd}|jdd|jdd|jdd|rtd|n|dk r|dk rtd ntj|}|dkrA|dkr|j}|j}q|}|j |}|j|krt d d |d ||qnN|j}||krqt d |d|n|jd||}|}t |t |fS(ss Maximum likelihood estimate for the location and scale parameters. `uniform.fit` uses only the following parameters. Because exact formulas are used, the parameters related to optimization that are available in the `fit` method of other distributions are ignored here. The only positional argument accepted is `data`. Parameters ---------- data : array_like Data to use in calculating the maximum likelihood estimate. floc : float, optional Hold the location parameter fixed to the specified value. fscale : float, optional Hold the scale parameter fixed to the specified value. Returns ------- loc, scale : float Maximum likelihood estimates for the location and scale. Notes ----- An error is raised if `floc` is given and any values in `data` are less than `floc`, or if `fscale` is given and `fscale` is less than ``data.max() - data.min()``. An error is also raised if both `floc` and `fscale` are given. Examples -------- >>> from scipy.stats import uniform We'll fit the uniform distribution to `x`: >>> x = np.array([2, 2.5, 3.1, 9.5, 13.0]) For a uniform distribution MLE, the location is the minimum of the data, and the scale is the maximum minus the minimum. >>> loc, scale = uniform.fit(x) >>> loc 2.0 >>> scale 11.0 If we know the data comes from a uniform distribution where the support starts at 0, we can use `floc=0`: >>> loc, scale = uniform.fit(x, floc=0) >>> loc 0.0 >>> scale 13.0 Alternatively, if we know the length of the support is 12, we can use `fscale=12`: >>> loc, scale = uniform.fit(x, fscale=12) >>> loc 1.5 >>> scale 12.0 In that last example, the support interval is [1.5, 13.5]. This solution is not unique. For example, the distribution with ``loc=2`` and ``scale=12`` has the same likelihood as the one above. When `fscale` is given and it is larger than ``data.max() - data.min()``, the parameters returned by the `fit` method center the support over the interval ``[data.min(), data.max()]``. isToo many arguments.RTRUR^R_RsUnknown arguments: %s.s3All parameters fixed. There is nothing to optimize.RRvRwRg?N( RRRRWRXR9RYRRR#RtRR( RR\RyR]RTRUR^R_R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR`Fs4I   "  ( R,R-R.RLR!R#R)R RRR`(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR (s       Rt vonmises_gencB`s;eZdZdZdZdZdZdZRS(sA Von Mises continuous random variable. %(before_notes)s Notes ----- The probability density function for `vonmises` and `vonmises_line` is: .. math:: f(x, \kappa) = \frac{ \exp(\kappa \cos(x)) }{ 2 \pi I_0(\kappa) } for :math:`-\pi \le x \le \pi`, :math:`\kappa > 0`. :math:`I_0` is the modified Bessel function of order zero (`scipy.special.i0`). `vonmises` is a circular distribution which does not restrict the distribution to a fixed interval. Currently, there is no circular distribution framework in scipy. The ``cdf`` is implemented such that ``cdf(x + 2*np.pi) == cdf(x) + 1``. `vonmises_line` is the same distribution, defined on :math:`[-\pi, \pi]` on the real line. This is a regular (i.e. non-circular) distribution. `vonmises` and `vonmises_line` take ``kappa`` as a shape parameter. %(after_notes)s %(example)s cC`s|jjd|d|jS(NgR(RItvonmisesRK(Rtkappa((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRLscC`s2tj|tj|dtjtj|S(Ni(R9R:RiRQR$ti0(RRR ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`stj||S(N(R t von_mises_cdf(RRR ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`sdS(Ni(iNiN(RW(RR ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _stats_skipscC`s@| tj|tj|tjdtjtj|S(Ni(R$ti1R R9RPRQ(RR ((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRR s(R,R-R.RLR!R#RRR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s     R t vonmises_linetwald_gencB`sDeZdZejZdZdZdZdZ dZ RS(sWA Wald continuous random variable. %(before_notes)s Notes ----- The probability density function for `wald` is: .. math:: f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp(- \frac{ (x-1)^2 }{ 2x }) for :math:`x > 0`. `wald` is a special case of `invgauss` with ``mu=1``. %(after_notes)s %(example)s cC`s|jjddd|jS(Ng?R(RIRRK(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRL+scC`stj|dS(Ng?(RR!(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!.scC`stj|dS(Ng?(RRM(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM2scC`stj|dS(Ng?(RR#(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#5scC`sdS(Ng?g@g.@(g?g?g@g.@((R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR 8s( R,R-R.RReRfRLR!RMR#R (((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRs     Rtwrapcauchy_gencB`s;eZdZdZdZdZdZdZRS(sA wrapped Cauchy continuous random variable. %(before_notes)s Notes ----- The probability density function for `wrapcauchy` is: .. math:: f(x, c) = \frac{1-c^2}{2\pi (1+c^2 - 2c \cos(x))} for :math:`0 \le x \le 2\pi`, :math:`0 < c < 1`. `wrapcauchy` takes ``c`` as a shape parameter for :math:`c`. %(after_notes)s %(example)s cC`s|dk|dk@S(Nii((RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&UscC`s8d||dtjd||d|tj|S(Ng?ii(R9RQRi(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!XscC`smtj|jd|j}d|d|}|tjk}d|}tj||}tj||}tj|rtj|tj||} dtj|}tj|d} ddtjtj | | } tj ||| ntj|ritj|tj||} tj|d} dtjtj | | }tj |||n|S(NRg?iig@( R9tzerosRRRQRRt ones_likeRRR(RRRRR-tc1Rtxptxntvalntyntontvalptyptop((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#\s$ "cC`sd|d|}dtj|tjtj|}dtjdtj|tjtjd|}tj|dk||S(Ng?iig?(R9RRRQR(RR(RR-trcqtrcmq((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)ps'6cC`s tjdtjd||S(Nii(R9RPRQ(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRvs(R,R-R.R&R!R#R)RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR?s     t wrapcauchyt gennorm_gencB`sVeZdZdZdZdZdZdZdZdZ dZ RS( sAA generalized normal continuous random variable. %(before_notes)s Notes ----- The probability density function for `gennorm` is [1]_: .. math:: f(x, \beta) = \frac{\beta}{2 \Gamma(1/\beta)} \exp(-|x|^\beta) :math:`\Gamma` is the gamma function (`scipy.special.gamma`). `gennorm` takes ``beta`` as a shape parameter for :math:`\beta`. For :math:`\beta = 1`, it is identical to a Laplace distribution. For :math:`\beta = 2`, it is identical to a normal distribution (with ``scale=1/sqrt(2)``). See Also -------- laplace : Laplace distribution norm : normal distribution References ---------- .. [1] "Generalized normal distribution, Version 1", https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1 %(example)s cC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s0tjd|tjd|t||S(Ng?g?(R9RPR$RR(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`s=dtj|}d||tjd|t||S(Ng?g?(R9RjR$RR(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`sCtj|d}|tjd|d|d||d|S(Ng?g?g@(R9RjR$R(RRRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`s|j| |S(N(R#(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`s|j|| S(N(R)(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+scC`sctjd|d|d|g\}}}dtj||dtj||d|dfS(Ng?g@g@gg@(R$RR9R:(RRRtc3tc5((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR s-cC`s*d|tjd|tjd|S(Ng?g?(R9RPR$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs( R,R-R.R!RMR#R)R&R+R RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR"}s!       tgennormthalfgennorm_gencB`sMeZdZdZdZdZdZdZdZdZ RS(sThe upper half of a generalized normal continuous random variable. %(before_notes)s Notes ----- The probability density function for `halfgennorm` is: .. math:: f(x, \beta) = \frac{\beta}{\Gamma(1/\beta)} \exp(-|x|^\beta) for :math:`x > 0`. :math:`\Gamma` is the gamma function (`scipy.special.gamma`). `gennorm` takes ``beta`` as a shape parameter for :math:`\beta`. For :math:`\beta = 1`, it is identical to an exponential distribution. For :math:`\beta = 2`, it is identical to a half normal distribution (with ``scale=1/sqrt(2)``). See Also -------- gennorm : generalized normal distribution expon : exponential distribution halfnorm : half normal distribution References ---------- .. [1] "Generalized normal distribution, Version 1", https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1 %(example)s cC`stj|j||S(N(R9R:RM(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`s&tj|tjd|||S(Ng?(R9RPR$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRMscC`stjd|||S(Ng?(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`stjd||d|S(Ng?(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)scC`stjd|||S(Ng?(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&scC`stjd||d|S(Ng?(R$R(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR+scC`s&d|tj|tjd|S(Ng?(R9RPR$R(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRs( R,R-R.R!RMR#R)R&R+RR(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&s#      t halfgennormtcrystalball_gencB`sDeZdZdZdZdZdZdZdZRS(s Crystalball distribution %(before_notes)s Notes ----- The probability density function for `crystalball` is: .. math:: f(x, \beta, m) = \begin{cases} N \exp(-x^2 / 2), &\text{for } x > -\beta\\ N A (B - x)^{-m} &\text{for } x \le -\beta \end{cases} where :math:`A = (m / |\beta|)^n \exp(-\beta^2 / 2)`, :math:`B = m/|\beta| - |\beta|` and :math:`N` is a normalisation constant. `crystalball` takes :math:`\beta > 0` and :math:`m > 1` as shape parameters. :math:`\beta` defines the point where the pdf changes from a power-law to a Gaussian distribution. :math:`m` is the power of the power-law tail. References ---------- .. [1] "Crystal Ball Function", https://en.wikipedia.org/wiki/Crystal_Ball_function %(after_notes)s .. versionadded:: 0.19.0 %(example)s cC`syd|||dtj|d dtt|}d}d}|t|| k|||fd|d|S( s` Return PDF of the crystalball function. -- | exp(-x**2 / 2), for x > -beta crystalball.pdf(x, beta, m) = N * | | A * (B - x)**(-m), for x <= -beta -- g?iig@cS`stj|d dS(Ni(R9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pytrhs4scS`s7|||tj|d d||||| S(Nig@(R9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pytlhs7s!R R(R9R:R;R@R (RRRRRR)R*((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!'s (  cC`sd|||dtj|d dtt|}d}d}tj|t|| k|||fd|d|S( sH Return the log of the PDF of the crystalball function. g?iig@cS`s |d dS(Ni((RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)DscS`s>|tj|||dd|tj||||S(Ni(R9RP(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR*GsR R(R9R:R;R@RPR (RRRRRR)R*((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRM=s (  cC`syd|||dtj|d dtt|}d}d}|t|| k|||fd|d|S( s8 Return CDF of the crystalball function g?iig@cS`s?||tj|d d|dtt|t| S(Nig@i(R9R:R;R@(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)Ss%cS`sC|||tj|d d||||| d|dS(Nig@i(R9R:(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR*WsR R(R9R:R;R@R (RRRRRR)R*((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#Ls (  cC`sd|||dtj|d dtt|}|||tj|d d|d}d}d}t||k|||fd|d|S( Ng?iig@cS`stj|d d}||||d}d|tt|}||||d||| |||dd|S(Nii(R9R:R;R@(RRRteb2tCR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pytppf_lessbs  cS`sktj|d d}||||d}d|tt|}tt| dt|||S(Nii(R9R:R;R@RD(RRRR+R,R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt ppf_greaterisR R(R9R:R;R@R (RRRRRtpbetaR-R.((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)]s (,  cC`sd|||dtj|d dtt|}d}|t|d|k|||ftj|dtjgtjS(sR Returns the n-th non-central moment of the crystalball function. g?iig@cS`s |||tj|d d}|||}d|ddtj|dddd|tj|dd|dd}tj|j}xct|dD]Q}|tj|||||d|||d||| |d7}qW|||S(s Returns n-th moment. Defined only if n+1 < m Function cannot broadcast due to the loop over n ig@ig?i( R9R:R$RRRRRstbinom(R RRtAtBR)R*R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt n_th_momentxs$$/2totypes(R9R:R;R@R t vectorizeRRc(RR RRRR3((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRqs ( cC`s|dk|dk@S(s@ Shape parameter bounds are m > 1 and beta > 0. ii((RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&s( R,R-R.R!RMR#R)RR&(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR(s#     t crystalballtlongnamesA Crystalball FunctioncC`st||t|dS(sh Utility function for the argus distribution used in the CDF and norm of the Argus Funktion g?(R@R<(R((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyt _argus_phist argus_gencB`s)eZdZdZdZdZRS(s Argus distribution %(before_notes)s Notes ----- The probability density function for `argus` is: .. math:: f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2} \exp(-\chi^2 (1 - x^2)/2) for :math:`0 < x < 1`, where .. math:: \Psi(\chi) = \Phi(\chi) - \chi \phi(\chi) - 1/2 with :math:`\Phi` and :math:`\phi` being the CDF and PDF of a standard normal distribution, respectively. `argus` takes :math:`\chi` as shape a parameter. References ---------- .. [1] "ARGUS distribution", https://en.wikipedia.org/wiki/ARGUS_distribution %(after_notes)s .. versionadded:: 0.19.0 %(example)s cC`sOd|d}|dtt||tj|tj|d |dS(s Return PDF of the argus function argus.pdf(x, chi) = chi**3 / (sqrt(2*pi) * Psi(chi)) * x * sqrt(1-x**2) * exp(- 0.5 * chi**2 * (1 - x**2)) g?ii(R;R8R9R[R:(RRRRz((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!scC`sd|j||S(s2 Return CDF of the argus function g?(R&(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#scC`s)t|tjd|dt|S(s@ Return survival function of the argus function ii(R8R9R[(RRR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR&s(R,R-R.R!R#R&(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR9s% targussAn Argus Functiont rv_histogramcB`sVeZdZejZdZdZdZdZdZ dZ dZ RS(s Generates a distribution given by a histogram. This is useful to generate a template distribution from a binned datasample. As a subclass of the `rv_continuous` class, `rv_histogram` inherits from it a collection of generic methods (see `rv_continuous` for the full list), and implements them based on the properties of the provided binned datasample. Parameters ---------- histogram : tuple of array_like Tuple containing two array_like objects The first containing the content of n bins The second containing the (n+1) bin boundaries In particular the return value np.histogram is accepted Notes ----- There are no additional shape parameters except for the loc and scale. The pdf is defined as a stepwise function from the provided histogram The cdf is a linear interpolation of the pdf. .. versionadded:: 0.19.0 Examples -------- Create a scipy.stats distribution from a numpy histogram >>> import scipy.stats >>> import numpy as np >>> data = scipy.stats.norm.rvs(size=100000, loc=0, scale=1.5, random_state=123) >>> hist = np.histogram(data, bins=100) >>> hist_dist = scipy.stats.rv_histogram(hist) Behaves like an ordinary scipy rv_continuous distribution >>> hist_dist.pdf(1.0) 0.20538577847618705 >>> hist_dist.cdf(2.0) 0.90818568543056499 PDF is zero above (below) the highest (lowest) bin of the histogram, defined by the max (min) of the original dataset >>> hist_dist.pdf(np.max(data)) 0.0 >>> hist_dist.cdf(np.max(data)) 1.0 >>> hist_dist.pdf(np.min(data)) 7.7591907244498314e-05 >>> hist_dist.cdf(np.min(data)) 0.0 PDF and CDF follow the histogram >>> import matplotlib.pyplot as plt >>> X = np.linspace(-5.0, 5.0, 100) >>> plt.title("PDF from Template") >>> plt.hist(data, density=True, bins=100) >>> plt.plot(X, hist_dist.pdf(X), label='PDF') >>> plt.plot(X, hist_dist.cdf(X), label='CDF') >>> plt.show() cO`s_||_t|dkr*tdntj|d|_tj|d|_t|jdt|jkrtdn|jd|jd |_|jttj |j|j|_tj |j|j|_ tj d|jdg|_tj d|j g|_ |jd|d<|jd|d (RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR!BscC`stj||j|jS(s3 CDF calculated from the histogram (R9tinterpR>RA(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR#HscC`stj||j|jS(sC Percentile function calculated from the histogram (R9RGRAR>(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR)NscC`sK|jd|d|jd |d|d}tj|jdd!|S(s$Compute the n-th non-central moment.ii(R>R9RR=(RR t integrals((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRTs0cC`sXt|jdd!dk|jdd!ftjd}tj|jdd!||j S(sCompute entropy of distributioniig(R R=R9RPRR?(RR((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRRYs  cC`s&tt|j}|j|d<|S(sF Set the histogram as additional constructor argument RC(RR;t_updated_ctor_paramR<(Rtdct((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyRIas ( R,R-R.RRfRzR!R#R)RRRRI(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyR;sC       (t __future__RRRRtnumpyR9tscipy.misc.doccerRRtscipyRRRt scipy.specialtspecialR$tscipy.special._ufuncst_ufuncsRtscipy._lib._numpy_compatRtscipy._lib._utilR R R|R t_tukeylambda_statsR RR Rt_distn_infrastructureRRRRRRRRt _constantsRRRRRRmtAttributeErrorRRR1R2R8R[RQR;RPR=R<R>R@RBRDRERFRGRHRaRbRgRhRmRnRsRXRtR~R{RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR R RRRRR R%R)R*RR+R/RIR0R2RLRJRKRMRQRRR^R_R`RaRxRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR3RRRSRVRYRZR\R]R^RbRdRfRgRhRiRkRlRwRxRzR{RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR RR R RRRRR!R"R%R&R'R(R6R8R9R:R;R tglobalstitemstpairst _distn_namest_distn_gen_namest__all__(((s=lib/python2.7/site-packages/scipy/stats/_continuous_distns.pyts  :(   64        W*%*)  ?44I/0=6#"79dI*2C#P 759 __0T, *:@0'28(20%*B3D5,,(.-3/1 23"3Y*4KH[B32'%1<0=*"F7F8;/ 1"(;"A> =!