# -*- coding: utf-8 -*-
"""
Created on Sun Sep 25 21:23:38 2011
Author: Josef Perktold and Scipy developers
License : BSD-3
"""
import numpy as np
from scipy import stats
from statsmodels.tools.validation import array_like, bool_like, int_like
[docs]def anderson_statistic(x, dist='norm', fit=True, params=(), axis=0):
"""
Calculate the Anderson-Darling a2 statistic.
Parameters
----------
x : array_like
The data to test.
dist : {'norm', callable}
The assumed distribution under the null of 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
The optional distribution parameters if fit is False.
axis : int
If dist is 'norm' or fit is False, then data can be an n-dimensional
and axis specifies the axis of a variable.
Returns
-------
{float, ndarray}
The Anderson-Darling statistic.
"""
x = array_like(x, 'x', ndim=None)
fit = bool_like(fit, 'fit')
axis = int_like(axis, 'axis')
y = np.sort(x, axis=axis)
nobs = 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:
raise ValueError("dist must be 'norm' or a Callable")
else:
if callable(dist):
z = dist.cdf(y, *params)
else:
raise ValueError('if fit is false, then dist must be callable')
i = np.arange(1, nobs + 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) / nobs * (np.log(z) + np.log1p(-z[sl2])),
axis=axis)
a2 = -nobs - s
return a2
[docs]def normal_ad(x, axis=0):
"""
Anderson-Darling test for normal distribution unknown mean and variance.
Parameters
----------
x : array_like
The data array.
axis : int
The axis to perform the test along.
Returns
-------
ad2 : float
Anderson Darling test statistic.
pval : float
The pvalue for hypothesis that the data comes from a normal
distribution with unknown mean and variance.
See Also
--------
statsmodels.stats.diagnostic.anderson_statistic
The Anderson-Darling a2 statistic.
statsmodels.stats.diagnostic.kstest_fit
Kolmogorov-Smirnov test with estimated parameters for Normal or
Exponential distributions.
"""
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, 0.1830])
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=False))
print(anderson_statistic(x, dist=stats.norm, fit=True))