M/PhndZddlZddlmZddZGddZGdd eZGd d eZdd Z dS)z Empirical CDF Functions N)interp1d皙?ct|}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 p/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/distributions/empirical_distribution.py _conf_setrsm, q66DgbfRX&&!d(344G GAKA & &E GAKA & &E %<c eZdZdZddZdZdS) 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|dvrd}t|||_tj|}tj|}|j|jkrd}t|t |jdkrd}t|tjtj |f|_ tj||f|_ |sYtj |j } tj |j | d|_ tj |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 ValueErrorsider asarrayshaperr_infxyargsorttaken) selfr"r#ivalsortedrmsg_x_yasorts r__init__zStepFunction.__init__Qs  ::<<0 0 0>CS// ! Z]] Z]] 8rx  6CS// ! rx==A  1CS// !w{#tRx /Jtv&&EWTVUA..DFWTVUA..DFarcbtj|j||jdz }|j|S)Nr)r searchsortedr"rr#)r'timetinds r__call__zStepFunction.__call__ks*tvtTY77!;vd|rN)rFr)__name__ __module__ __qualname____doc__r.r3rrrr%sB))V!!!!4rrc$eZdZdZdfd ZxZS)ECDFa Return the Empirical CDF of an array as a step function. Parameters ---------- x : array_like Observations side : {'left', 'right'}, optional Default is 'right'. Defines the shape of the intervals constituting the steps. 'right' correspond to [a, b) intervals and 'left' to (a, b]. Returns ------- Empirical CDF as a step function. Examples -------- >>> import numpy as np >>> from statsmodels.distributions.empirical_distribution import ECDF >>> >>> ecdf = ECDF([3, 3, 1, 4]) >>> >>> ecdf([3, 55, 0.5, 1.5]) array([ 0.75, 1. , 0. , 0.25]) rctj|d}|t|}tjd|z d|}t |||ddS)NT)copyg?rrr))r arraysortrlinspacesuperr.)r'r"rrr# __class__s rr.z ECDF.__init__sm HQT " " " 1vv K4D ) ) AD66666r)rr4r5r6r7r. __classcell__rBs@rr:r:qsG27777777777rr:c$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. ] Nrc|tj|d\}}ntj|}t|t|ksJtj|}tj|}|dksJ|}||}tj||}||z }t|||ddS)NT) return_countsrr=) r uniquerrsumr$cumsumrAr.) r'r" freq_weightsrwswaxr#rBs rr.zECDFDiscrete.__init__s   i>>>OA|| 1 A<  CFF**** J| $ $ VAYYAvvvv YY[[ bE Iae   F AD66666r)NrrCrEs@rrGrGsH//` 7 7 7 7 7 7 7 7 7 7rrGTc tj|}|r ||fi|}n7g}|D]}|||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. )r rappendr>r$r)fnr" vectorizedkeywordsr#r+as rmonotone_fn_inverterrWs 1 A Bq  H    ) )B HHRR''h'' ( ( ( ( HQKK 1 A AaD!A$  r)r)T) r7numpyr scipy.interpolaterrrr:rGrWr8rrrZs&&&&&&:IIIIIIIIX77777<777P>7>7>7>7>7<>7>7>7B      r