DjYldZddlZddlmZd dZGddZGddeZGd d eZd d Z y)z Empirical CDF Functions N)interp1dct|}tjtjd|z d|zz }tj||z dd}tj||zdd}||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)lennpsqrtlogclip)Falphanobsepsilonloweruppers tC:\Crop_Prediction\Backend\crop-ai-system\venv\Lib\site-packages\statsmodels/distributions/empirical_distribution.py _conf_setrsg, q6DggbffRX&!d(34G GGAKA &E GGAKA &E %<ceZdZdZddZdZy) 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 c|jdvr d}t|||_tj|}tj|}|j |j k7r d}t|t |j dk7r d}t|tjtj |f|_ tj||f|_ |sktj|j} tj|j| d|_ tj|j| d|_ |jj d|_ y)N)rightleftz*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 ValueErrorsiderasarrayshaperr_infxyargsorttaken) selfr r!ivalsortedrmsg_x_yasorts r__init__zStepFunction.__init__Qs ::<0 0>CS/ ! ZZ] ZZ] 88rxx 6CS/ ! rxx=A 1CS/ !w{#tRxJJtvv&EWWTVVUA.DFWWTVVUA.DFarc|tj|j||jdz }|j|S)Nr)r searchsortedr rr!)r%timetinds r__call__zStepFunction.__call__ks/tvvtTYY7!;vvd|rN)gFr)__name__ __module__ __qualname____doc__r,r1rrrr%s)V!4rrc$eZdZdZdfd ZxZS)ECDFa Return the Empirical CDF of an array as a step function. Parameters ---------- x : array_like Observations side : {'left', 'right'}, optional Default is 'right'. Defines the shape of the intervals constituting the steps. 'right' correspond to [a, b) intervals and 'left' to (a, b]. Returns ------- Empirical CDF as a step function. Examples -------- >>> import numpy as np >>> from statsmodels.distributions.empirical_distribution import ECDF >>> >>> ecdf = ECDF([3, 3, 1, 4]) >>> >>> ecdf([3, 55, 0.5, 1.5]) array([ 0.75, 1. , 0. , 0.25]) ctj|d}|jt|}tjd|z d|}t ||||dy)NT)copyg?rrr')rarraysortrlinspacesuperr,)r%r rrr! __class__s rr,z ECDF.__init__sQ HHQT " 1v KK4D ) AD6r)rr2r3r4r5r, __classcell__r@s@rr8r8qs277rr8c$eZdZdZdfd ZxZS) ECDFDiscreteaZ Return the Empirical Weighted CDF of an array as a step function. Parameters ---------- x : array_like Data values. If freq_weights is None, then x is treated as observations and the ecdf is computed from the frequency counts of unique values using nunpy.unique. If freq_weights is not None, then x will be taken as the support of the mass point distribution with freq_weights as counts for x values. The x values can be arbitrary sortable values and need not be integers. freq_weights : array_like Weights of the observations. sum(freq_weights) is interpreted as nobs for confint. If freq_weights is None, then the frequency counts for unique values will be computed from the data x. 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 ------- Weighted ECDF as a step function. Examples -------- >>> import numpy as np >>> from statsmodels.distributions.empirical_distribution import ( >>> ECDFDiscrete) >>> >>> ewcdf = ECDFDiscrete([3, 3, 1, 4]) >>> ewcdf([3, 55, 0.5, 1.5]) array([0.75, 1. , 0. , 0.25]) >>> >>> ewcdf = ECDFDiscrete([3, 1, 4], [1.25, 2.5, 5]) >>> >>> ewcdf([3, 55, 0.5, 1.5]) array([0.42857143, 1., 0. , 0.28571429]) >>> print('e1 and e2 are equivalent ways of defining the same ECDF') e1 and e2 are equivalent ways of defining the same ECDF >>> e1 = ECDFDiscrete([3.5, 3.5, 1.5, 1, 4]) >>> e2 = ECDFDiscrete([3.5, 1.5, 1, 4], freq_weights=[2, 1, 1, 1]) >>> print(e1.x, e2.x) [-inf 1. 1.5 3.5 4. ] [-inf 1. 1.5 3.5 4. ] >>> print(e1.y, e2.y) [0. 0.2 0.4 0.8 1. ] [0. 0.2 0.4 0.8 1. ] c|tj|d\}}ntj|}t|t|k(sJtj|}tj|}|dkDsJ|j }||}tj ||}||z }t|!|||dy)NT) return_countsrr;) runiquerrsumr"cumsumr?r,) r%r freq_weightsrwswaxr!r@s rr,zECDFDiscrete.__init__s   ii>OA| 1 A< CF** JJ| $ VVAYAv YY[ bE IIae  F AD6r)NrrArCs@rrErEs/` 7 7rrEc tj|}|r ||fi|}n6g}|D]}|j||fi|tj|}tj|}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<r"r)fnr vectorizedkeywordsr!r)as rmonotone_fn_inverterrUs| 1 A q H   )B HHR'h' ( ) HHQK 1 A AaD!A$ r)g?)T) r5numpyrscipy.interpolaterrrr8rErUr6rrrXsC&:IIX7<7P>7<>7B r