Source code for statsmodels.stats._adnorm

"""
Created on Sun Sep 25 21:23:38 2011

Author: Josef Perktold and Scipy developers
License : BSD-3
"""
import warnings

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)
        elif callable(dist):
            params = dist.fit(x)
            z = dist.cdf(y, *params)
        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)
    with warnings.catch_warnings():
        warnings.filterwarnings(
            "ignore", message="divide by zero encountered in log1p"
        )
        ad_values = (2 * i[sl1] - 1.0) / nobs * (np.log(z) + np.log1p(-z[sl2]))
        s = np.sum(ad_values, 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