Source code for statsmodels.stats._adnorm

# -*- coding: utf-8 -*-
"""
Created on Sun Sep 25 21:23:38 2011

Author: Josef Perktold and Scipy developers
License : BSD-3
"""
from __future__ import print_function
from statsmodels.compat.python import range
import numpy as np
from scipy import stats

from numpy import exp

def anderson_statistic(x, dist='norm', fit=True, params=(), axis=0):
    '''calculate anderson-darling A2 statistic

    Parameters
    ----------
    x : array_like
        data
    dist : 'norm' or callable
        null distribution for the test statistic
    fit : bool
        If True, then the distribution parameters are estimated.
        Currently only for 1d data x, except in case dist='norm'
    params : tuple
        optional distribution parameters if fit is False
    axis : integer
        If dist is 'norm' or fit is False, then data can be an n-dimensional
        and axis specifies the axis of a variable

    Returns
    -------
    ad2 : float or ndarray
        Anderson-Darling statistic


    '''
    x = np.asarray(x)
    y = np.sort(x, axis=axis)
    N = y.shape[axis]
    if fit:
        if dist == 'norm':
            xbar = np.expand_dims(np.mean(x, axis=axis), axis)
            s = np.expand_dims(np.std(x, ddof=1, axis=axis), axis)
            w = (y-xbar)/s
            z = stats.norm.cdf(w)
            #print z
        elif callable(dist):
            params = dist.fit(x)
            #print params
            z = dist.cdf(y, *params)
            print(z)
    else:
        if callable(dist):
            z = dist.cdf(y, *params)
        else:
            raise ValueError('if fit is false, then dist needs to be callable')

    i = np.arange(1,N+1)
    sl1 = [None]*x.ndim
    sl1[axis] = slice(None)
    sl1 = tuple(sl1)
    sl2 = [slice(None)]*x.ndim
    sl2[axis] = slice(None,None,-1)
    sl2 = tuple(sl2)
    S = np.sum((2*i[sl1]-1.0)/N*(np.log(z)+np.log(1-z[sl2])), axis=axis)
    A2 = -N-S
    return A2


[docs]def normal_ad(x, axis=0): '''Anderson-Darling test for normal distribution unknown mean and variance Parameters ---------- x : array_like data array, currently only 1d Returns ------- ad2 : float Anderson Darling test statistic pval : float pvalue for hypothesis that the data comes from a normal distribution with unknown mean and variance ''' #ad2 = stats.anderson(x)[0] ad2 = anderson_statistic(x, dist='norm', fit=True, axis=axis) n = x.shape[axis] ad2a = ad2 * (1 + 0.75/n + 2.25/n**2) if np.size(ad2a) == 1: if (ad2a >= 0.00 and ad2a < 0.200): pval = 1 - np.exp(-13.436 + 101.14 * ad2a - 223.73 * ad2a**2) elif ad2a < 0.340: pval = 1 - np.exp(-8.318 + 42.796 * ad2a - 59.938 * ad2a**2) elif ad2a < 0.600: pval = np.exp(0.9177 - 4.279 * ad2a - 1.38 * ad2a**2) elif ad2a <= 13: pval = np.exp(1.2937 - 5.709 * ad2a + 0.0186 * ad2a**2) else: pval = 0.0 # is < 4.9542108058458799e-31 else: bounds = np.array([0.0, 0.200, 0.340, 0.600]) pval0 = lambda ad2a: np.nan*np.ones_like(ad2a) pval1 = lambda ad2a: 1 - np.exp(-13.436 + 101.14 * ad2a - 223.73 * ad2a**2) pval2 = lambda ad2a: 1 - np.exp(-8.318 + 42.796 * ad2a - 59.938 * ad2a**2) pval3 = lambda ad2a: np.exp(0.9177 - 4.279 * ad2a - 1.38 * ad2a**2) pval4 = lambda ad2a: np.exp(1.2937 - 5.709 * ad2a + 0.0186 * ad2a**2) pvalli = [pval0, pval1, pval2, pval3, pval4] idx = np.searchsorted(bounds, ad2a, side='right') pval = np.nan*np.ones_like(ad2a) for i in range(5): mask = (idx == i) pval[mask] = pvalli[i](ad2a[mask]) return ad2, pval
if __name__ == '__main__': x = np.array([-0.1184, -1.3403, 0.0063, -0.612 , -0.3869, -0.2313, -2.8485, -0.2167, 0.4153, 1.8492, -0.3706, 0.9726, -0.1501, -0.0337, -1.4423, 1.2489, 0.9182, -0.2331, -0.6182, 0.183 ]) r_res = np.array([0.58672353588821502, 0.1115380760041617]) ad2, pval = normal_ad(x) print(ad2, pval) print(r_res - [ad2, pval]) print(anderson_statistic((x-x.mean())/x.std(), dist=stats.norm, fit=0)) print(anderson_statistic(x, dist=stats.norm, fit=True))