# -*- 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
[docs]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 hasattr(dist, '__call__'):
params = dist.fit(x)
#print params
z = dist.cdf(y, *params)
print(z)
else:
if hasattr(dist, '__call__'):
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)
sl2 = [slice(None)]*x.ndim
sl2[axis] = slice(None,None,-1)
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))