B Z@sdZddlZddlmZdddZGdddeZGd d d eZdd d Z e dkrddl m Z ddl mZe dZeeZedZeeZeeeZejeeddee\ZZejeedddejeedddeddeddeeddedS)z Empirical CDF Functions N)interp1d皙?cCsPt|}ttd|d|}t||dd}t||dd}||fS)a Constructs a Dvoretzky-Kiefer-Wolfowitz confidence band for the eCDF. Parameters ---------- F : array-like The empirical distributions alpha : float Set alpha for a (1 - alpha) % confidence band. Notes ----- Based on the DKW inequality. .. math:: P \left( \sup_x \left| F(x) - \hat(F)_n(X) \right| > \epsilon \right) \leq 2e^{-2n\epsilon^2} References ---------- Wasserman, L. 2006. `All of Nonparametric Statistics`. Springer. g@r)lennpZsqrtlogZclip)FZalphanobsepsilonlowerupperrOlib/python3.7/site-packages/statsmodels/distributions/empirical_distribution.py _conf_sets rc@s"eZdZdZd ddZddZd S) StepFunctiona/ A basic step function. Values at the ends are handled in the simplest way possible: everything to the left of x[0] is set to ival; everything to the right of x[-1] is set to y[-1]. Parameters ---------- x : array-like y : array-like ival : float ival is the value given to the values to the left of x[0]. Default is 0. sorted : bool Default is False. side : {'left', 'right'}, optional Default is 'left'. Defines the shape of the intervals constituting the steps. 'right' correspond to [a, b) intervals and 'left' to (a, b]. Examples -------- >>> import numpy as np >>> from statsmodels.distributions.empirical_distribution import StepFunction >>> >>> x = np.arange(20) >>> y = np.arange(20) >>> f = StepFunction(x, y) >>> >>> print(f(3.2)) 3.0 >>> print(f([[3.2,4.5],[24,-3.1]])) [[ 3. 4.] [ 19. 0.]] >>> f2 = StepFunction(x, y, side='right') >>> >>> print(f(3.0)) 2.0 >>> print(f2(3.0)) 3.0 Fleftc Cs|dkrd}t|||_t|}t|}|j|jkrJd}t|t|jdkrdd}t|tjtj |f|_ tj||f|_ |st |j } t |j | d|_ t |j | d|_ |j jd|_ dS)N)rightrz*side can take the values 'right' or 'left'z"x and y do not have the same shaperzx and y must be 1-dimensionalr)r ValueErrorsiderasarrayshaperZr_infxyargsortZtaken) selfrrivalsortedrmsg_xZ_yZasortrrr__init__Ms&     zStepFunction.__init__cCs t|j||jd}|j|S)Nr)rZ searchsortedrrr)rZtimeZtindrrr__call__gszStepFunction.__call__N)rFr)__name__ __module__ __qualname____doc__r#r$rrrrr"s) rcs"eZdZdZdfdd ZZS)ECDFa Return the Empirical CDF of an array as a step function. Parameters ---------- x : array-like Observations side : {'left', 'right'}, optional Default is 'right'. Defines the shape of the intervals constituting the steps. 'right' correspond to [a, b) intervals and 'left' to (a, b]. Returns ------- Empirical CDF as a step function. Examples -------- >>> import numpy as np >>> from statsmodels.distributions.empirical_distribution import ECDF >>> >>> ecdf = ECDF([3, 3, 1, 4]) >>> >>> ecdf([3, 55, 0.5, 1.5]) array([ 0.75, 1. , 0. , 0.25]) rcsfd}|rRtj|dd}|t|}td|d|}tt|j|||ddnt||dt dSdS)NT)copyg?r)rr F)Z drop_errorsZ fill_values) rarraysortrZlinspacesuperr)r#rr)rrrstepr r) __class__rrr#sz ECDF.__init__)r)r%r&r'r(r# __classcell__rr)r/rr)lsr)TcKsft|}|r||f|}n.g}x|D]}|||f|q&Wt|}t|}t||||S)z Given a monotone function fn (no checking is done to verify monotonicity) and a set of x values, return an linearly interpolated approximation to its inverse from its values on x. )rrappendr+rr)fnrZ vectorizedkeywordsrr"arrrmonotone_fn_inverters    r5__main__)urlopenz-http://www.statsci.org/data/general/nerve.txtgI@Zpost)whererg?g?)r)T)r(ZnumpyrZscipy.interpolaterrobjectrr)r5r%Zstatsmodels.compat.pythonr7Zmatplotlib.pyplotZpyplotZpltZ nerve_dataZloadtxtrZcdfr,r r.r r ZxlimZylimZvlinesZshowrrrrs.  J%