U md@s^dZddlZddlmZdddZGdddZGd d d eZGd d d eZdddZ dS)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)lennpsqrtlogZclip)Falphanobsepsilonlowerupperri/home/sam/Atlas/atlas_env/lib/python3.8/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) selfrrZivalsortedrmsg_xZ_yZasortrrr__init__Qs&     zStepFunction.__init__cCs t|j||jd}|j|S)Nr)rZ searchsortedrrr)r timeZtindrrr__call__kszStepFunction.__call__N)rFr)__name__ __module__ __qualname____doc__r$r&rrrrr%s+ rcs"eZdZdZdfdd ZZS)ECDFa Return the Empirical CDF of an array as a step function. Parameters ---------- x : array_like Observations side : {'left', 'right'}, optional Default is 'right'. Defines the shape of the intervals constituting the steps. 'right' correspond to [a, b) intervals and 'left' to (a, b]. Returns ------- Empirical CDF as a step function. Examples -------- >>> import numpy as np >>> from statsmodels.distributions.empirical_distribution import ECDF >>> >>> ecdf = ECDF([3, 3, 1, 4]) >>> >>> ecdf([3, 55, 0.5, 1.5]) array([ 0.75, 1. , 0. , 0.25]) rcsLtj|dd}|t|}td|d|}tt|j|||dddS)NT)copyg?rrr!)rarraysortrZlinspacesuperr+r$)r rrr r __class__rrr$s z ECDF.__init__)rr'r(r)r*r$ __classcell__rrr1rr+qsr+cs"eZdZdZdfdd ZZS) 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. ] Nrcs|dkrtj|dd\}}n t|}t|t|ks:tt|}t|}|dksZt|}||}t||}||}tt |j |||dddS)NT)Z return_countsrr-) runiquerrAssertionErrorsumrZcumsumr0r5r$)r rZ freq_weightsrwswZaxrr1rrr$s    zECDFDiscrete.__init__)Nrr3rrr1rr5s0r5TcKsbt|}|r||f|}n*g}|D]}|||f|q$t|}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   r?)r)T) r*numpyrZscipy.interpolaterrrr+r5r?rrrrs  L(A