`scipy.stats._morestats:anderson`

source: /scipy/stats/_morestats.py:2369

Signature

def anderson(x, dist = norm, *, method = None)

Summary

Anderson-Darling test for data coming from a particular distribution.

Extended Summary

The Anderson-Darling test tests the null hypothesis that a sample is drawn from a population that follows a particular distribution. For the Anderson-Darling test, the critical values depend on which distribution is being tested against. This function works for normal, exponential, logistic, weibull_min, or Gumbel (Extreme Value Type I) distributions.

Parameters

x : array_like: Array of sample data.
dist : {'norm', 'expon', 'logistic', 'gumbel', 'gumbel_l', 'gumbel_r', 'extreme1', 'weibull_min'}, optional: The type of distribution to test against. The default is 'norm'. The names 'extreme1', 'gumbel_l' and 'gumbel' are synonyms for the same distribution.
method : str or instance of `MonteCarloMethod`: Defines the method used to compute the p-value. If method is "interpolated", the p-value is interpolated from pre-calculated tables. If method is an instance of MonteCarloMethod, the p-value is computed using scipy.stats.monte_carlo_test with the provided configuration options and other appropriate settings.
versionadded 1.17.0
If method is not specified, anderson will emit a FutureWarning specifying that the user must opt into a p-value calculation method. When method is specified, the object returned will include a pvalue attribute, but no critical_value, significance_level, or fit_result attributes. Beginning in 1.19.0, these other attributes will no longer be available, and a p-value will always be computed according to one of the available method options.

Returns

result : AndersonResult

If method is provided, this is an object with the following attributes:

statistic: The Anderson-Darling test statistic.
pvalue: float: The p-value corresponding with the test statistic, calculated according to the specified method.

If method is unspecified, this is an object with the following attributes:

statistic: The Anderson-Darling test statistic.
critical_values: The critical values for this distribution.
significance_level: The significance levels for the corresponding critical values in percents. The function returns critical values for a differing set of significance levels depending on the distribution that is being tested against.
fit_result: An object containing the results of fitting the distribution to the data.

Notes

Critical values provided when method is unspecified are for the following significance levels:

normal/exponential: 15%, 10%, 5%, 2.5%, 1%
logistic: 25%, 10%, 5%, 2.5%, 1%, 0.5%
gumbel_l / gumbel_r: 25%, 10%, 5%, 2.5%, 1%
weibull_min: 50%, 25%, 15%, 10%, 5%, 2.5%, 1%, 0.5%

If the returned statistic is larger than these critical values then for the corresponding significance level, the null hypothesis that the data come from the chosen distribution can be rejected. The returned statistic is referred to as 'A2' in the references.

For weibull_min, maximum likelihood estimation is known to be challenging. If the test returns successfully, then the first order conditions for a maximum likelihood estimate have been verified and the critical values correspond relatively well to the significance levels, provided that the sample is sufficiently large (>10 observations [7]). However, for some data - especially data with no left tail - anderson is likely to result in an error message. In this case, consider performing a custom goodness of fit test using scipy.stats.monte_carlo_test.

Examples

Test the null hypothesis that a random sample was drawn from a normal distribution (with unspecified mean and standard deviation).

import numpy as np
from scipy.stats import anderson
rng = np.random.default_rng(9781234521)
data = rng.random(size=35)
res = anderson(data, dist='norm', method='interpolate')
res.statistic
res.pvalue

✓

np.float64(0.012111200538380142)

The p-value is approximately 0.012,, so the null hypothesis may be rejected at a significance level of 2.5%, but not at a significance level of 1%.

Aliases

scipy.stats.anderson