ó î&]\c @`s’dZddlmZmZmZddddddd d d d g Zdd lZddlmZm Z m Z dd l j Z ddl m Z ddlmZddlmZmZmZmZedddgƒd ed„Zded„Zedddgƒd d„Zd#eefdd d„Zdddgd d„Zdddgdd d„Zdd d„Z d d „Z!d d!„Z"d d"„Z#d S($sB Additional statistics functions with support for masked arrays. i(tdivisiontprint_functiontabsolute_importtcompare_medians_mst hdquantilesthdmedianthdquantiles_sdt idealfourthst median_cihstmjcitmquantiles_cimjtrshttrimmed_mean_ciN(tfloat_tint_tndarray(t MaskedArrayi(t mstats_basic(tnormtbetatttbinomgÐ?gà?gè?cC`sÂd„}tj|dtdtƒ}tj|dtddƒ}|dksZ|jdkro||||ƒ}n@|jdkr”td|jƒ‚ntj|||||ƒ}tj |dtƒS( s Computes quantile estimates with the Harrell-Davis method. The quantile estimates are calculated as a weighted linear combination of order statistics. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdquantiles : MaskedArray A (p,) array of quantiles (if `var` is False), or a (2,p) array of quantiles and variances (if `var` is True), where ``p`` is the number of quantiles. See Also -------- hdquantiles_sd c S`s¬tjtj|jƒjtƒƒƒ}|j}tjdt|ƒft ƒ}|dkrxtj |_ |rp|S|dStj |dƒt |ƒ}tj}x˜t|ƒD]Š\}} |||d| |dd| ƒ} | d| d } tj| |ƒ} | |d|fs,'    &(-tcopytdtypetndminiisDArray 'data' must be at most two dimensional, but got data.ndim = %dN( tmatarraytFalseR RtNonetndimt ValueErrortapply_along_axist fix_invalid(R%R&taxisR'R2R.tresult((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyRs iÿÿÿÿcC`s(t|dgd|d|ƒ}|jƒS(s9 Returns the Harrell-Davis estimate of the median along the given axis. Parameters ---------- data : ndarray Data array. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdmedian : MaskedArray The median values. If ``var=True``, the variance is returned inside the masked array. E.g. for a 1-D array the shape change from (1,) to (2,). gà?R>R'(RR(R%R>R'R?((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyRjscC`s³d„}tj|dtdtƒ}tj|dtddƒ}|dkr]|||ƒ}n=|jdkr‚td|jƒ‚ntj||||ƒ}tj |dtƒj ƒS( sý The standard error of the Harrell-Davis quantile estimates by jackknife. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- hdquantiles_sd : MaskedArray Standard error of the Harrell-Davis quantile estimates. See Also -------- hdquantiles c S`s¶tj|jƒƒ}t|ƒ}tjt|ƒtƒ}|dkrTtj|_ntj|ƒt |dƒ}t j }x5t |ƒD]'\}}|||d||dd|ƒ} | d| d } tj gt|ƒD]T} tj| |tjttd| ƒƒtt| d|ƒƒfjtƒƒ^qÞdtƒ} tj| jƒdtddƒ|t |dƒ} t |dƒtjtj| ƒjƒt |ƒƒ||R3R4R5iisDArray 'data' must be at most two dimensional, but got data.ndim = %dN( R6R7R8R RR9R:R;R<R=travel(R%R&R>RMR.R?((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyR„s  gš™™™™™É?gš™™™™™©?c C`s¶tj|dtƒ}tj|d|d|d|ƒ}|j|ƒ}tj|d|d|d|ƒ}|j|ƒd}tj d|d|ƒ} t j|| ||| |fƒS(s³ Selected confidence interval of the trimmed mean along the given axis. Parameters ---------- data : array_like Input data. limits : {None, tuple}, optional None or a two item tuple. Tuple of the percentages to cut on each side of the array, with respect to the number of unmasked data, as floats between 0. and 1. If ``n`` is the number of unmasked data before trimming, then (``n * limits[0]``)th smallest data and (``n * limits[1]``)th largest data are masked. The total number of unmasked data after trimming is ``n * (1. - sum(limits))``. The value of one limit can be set to None to indicate an open interval. Defaults to (0.2, 0.2). inclusive : (2,) tuple of boolean, optional If relative==False, tuple indicating whether values exactly equal to the absolute limits are allowed. If relative==True, tuple indicating whether the number of data being masked on each side should be rounded (True) or truncated (False). Defaults to (True, True). alpha : float, optional Confidence level of the intervals. Defaults to 0.05. axis : int, optional Axis along which to cut. If None, uses a flattened version of `data`. Defaults to None. Returns ------- trimmed_mean_ci : (2,) ndarray The lower and upper confidence intervals of the trimmed data. R3tlimitst inclusiveR>ig@( R6R7R8tmstatsttrimrtmeant trimmed_stdetcountRtppfR( R%RORPtalphaR>ttrimmedttmeanttstdetdfttppf((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyR Ás*!!cC`s‘d„}tj|dtƒ}|jdkrCtd|jƒ‚ntj|dtddƒ}|dkrw|||ƒStj||||ƒSdS(s„ Returns the Maritz-Jarrett estimators of the standard error of selected experimental quantiles of the data. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. c S`s#tj|jƒƒ}|j}tj|ƒ|djtƒ}tj}tj t |ƒt ƒ}tj d|ddt ƒ|}|d|}xt |ƒD]\}} ||| d|| ƒ||| d|| ƒ} tj| |ƒ} tj| |dƒ} tj| | dƒ||RdR.((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyR ôs   c C`s}t|d|ƒ}tjd|dƒ}tj||ddddd|ƒ}t||d|ƒ}||||||fS(sÕ Computes the alpha confidence interval for the selected quantiles of the data, with Maritz-Jarrett estimators. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. alpha : float, optional Confidence level of the intervals. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- ci_lower : ndarray The lower boundaries of the confidence interval. Of the same length as `prob`. ci_upper : ndarray The upper boundaries of the confidence interval. Of the same length as `prob`. ig@talphapitbetapR>(tminRRVRQt mquantilesR (R%R&RWR>tztxqtsmj((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyR !s $cC`s}d„}tj|dtƒ}|dkr<|||ƒ}n=|jdkratd|jƒ‚ntj||||ƒ}|S(sA Computes the alpha-level confidence interval for the median of the data. Uses the Hettmasperger-Sheather method. Parameters ---------- data : array_like Input data. Masked values are discarded. The input should be 1D only, or `axis` should be set to None. alpha : float, optional Confidence level of the intervals. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- median_cihs Alpha level confidence interval. c S`sŽtj|jƒƒ}t|ƒ}t|d|ƒ}ttj|d|dƒƒ}tj|||dƒtj|d|dƒ}|d|krÐ|d8}tj|||dƒtj|d|dƒ}ntj||d|dƒtj||dƒ}|d|||}|||t ||d||ƒ}|||d|||d||||dd||||f}|S(Nig@gà?i( RRRRRgtintRt_ppfR"R!( R%RWR)RJtgktgkktItlambdtlims((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyt_cihs_1DZs 0 30(-R3isDArray 'data' must be at most two dimensional, but got data.ndim = %dN(R6R7R8R9R:R;R<(R%RWR>RsR?((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyRCs  cC`s“tj|d|ƒtj|d|ƒ}}tj|d|ƒtj|d|ƒ}}tj||ƒtj|d|dƒ}dtj|ƒS(s+ Compares the medians from two independent groups along the given axis. The comparison is performed using the McKean-Schrader estimate of the standard error of the medians. Parameters ---------- group_1 : array_like First dataset. Has to be of size >=7. group_2 : array_like Second dataset. Has to be of size >=7. axis : int, optional Axis along which the medians are estimated. If None, the arrays are flattened. If `axis` is not None, then `group_1` and `group_2` should have the same shape. Returns ------- compare_medians_ms : {float, ndarray} If `axis` is None, then returns a float, otherwise returns a 1-D ndarray of floats with a length equal to the length of `group_1` along `axis`. R>ii( R6tmedianRQt stde_medianRtabsRERR"(tgroup_1tgroup_2R>tmed_1tmed_2tstd_1tstd_2Ra((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyRvs +,cC`sTd„}tj|d|ƒjtƒ}|dkr=||ƒStj|||ƒSdS(sC Returns an estimate of the lower and upper quartiles. Uses the ideal fourths algorithm. Parameters ---------- data : array_like Input array. axis : int, optional Axis along which the quartiles are estimated. If None, the arrays are flattened. Returns ------- idealfourths : {list of floats, masked array} Returns the two internal values that divide `data` into four parts using the ideal fourths algorithm either along the flattened array (if `axis` is None) or along `axis` of `data`. cS`sµ|jƒ}t|ƒ}|dkr4tjtjgSt|dddƒ\}}t|ƒ}d|||d|||}||}d||||||d}||gS(Nig@ig(@ig«ªªªªªÚ?(RRRRtdivmodRl(R%R^R)tjthtqloRJtqup((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyt_idf­s    " "R>N(R6RRRR9R<(R%R>R‚((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyR—s    cC`s%tj|dtƒ}|d kr*|}ntj|dtddƒ}|jdkrctdƒ‚n|jƒ}t|dd ƒ}d|d|d|d }|d d …d f|d d d …f|kj dƒ}|d d …d f|d d d …f|kj dƒ}||d ||S(sé Evaluates Rosenblatt's shifted histogram estimators for each data point. Rosenblatt's estimator is a centered finite-difference approximation to the derivative of the empirical cumulative distribution function. Parameters ---------- data : sequence Input data, should be 1-D. Masked values are ignored. points : sequence or None, optional Sequence of points where to evaluate Rosenblatt shifted histogram. If None, use the data. R3R5is#The input array should be 1D only !R>g333333ó?iÿÿÿÿigð?iNg@gš™™™™™É?( R6R7R8R9RR:tAttributeErrorRURtsum(R%tpointsR)trRtnhitnlo((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyR ¿s   99(gš™™™™™É?gš™™™™™É?($t__doc__t __future__RRRt__all__tnumpyRR RRtnumpy.maR6RtRRQtscipy.stats.distributionsRRRRRCR9R8RRRtTrueR R R RRRR (((s8lib/python2.7/site-packages/scipy/stats/mstats_extras.pyts0    "!K= 2-"3 ! (