scipy.stats.

anderson#

scipy.stats.anderson(x, dist='norm', *, method='interpolate')[source]#

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

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:
xarray_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.

methodstr 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 (without extrapolating). 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.

Returns:
resultAndersonResult

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

statisticfloat

The Anderson-Darling test statistic.

pvalue: float

The p-value corresponding with the test statistic, calculated according to the specified method.

See also

kstest

The Kolmogorov-Smirnov test for goodness-of-fit.

Notes

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.

References

[2]

Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and Some Comparisons, Journal of the American Statistical Association, Vol. 69, pp. 730-737.

[3]

Stephens, M. A. (1976). Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters, Annals of Statistics, Vol. 4, pp. 357-369.

[4]

Stephens, M. A. (1977). Goodness of Fit for the Extreme Value Distribution, Biometrika, Vol. 64, pp. 583-588.

[5]

Stephens, M. A. (1977). Goodness of Fit with Special Reference to Tests for Exponentiality , Technical Report No. 262, Department of Statistics, Stanford University, Stanford, CA.

[6]

Stephens, M. A. (1979). Tests of Fit for the Logistic Distribution Based on the Empirical Distribution Function, Biometrika, Vol. 66, pp. 591-595.

[7]

Richard A. Lockhart and Michael A. Stephens “Estimation and Tests of Fit for the Three-Parameter Weibull Distribution” Journal of the Royal Statistical Society.Series B(Methodological) Vol. 56, No. 3 (1994), pp. 491-500, Table 0.

[8]

D’Agostino, Ralph B. (1986). “Tests for the Normal Distribution”. In: Goodness-of-Fit Techniques. Ed. by Ralph B. D’Agostino and Michael A. Stephens. New York: Marcel Dekker, pp. 122-141. ISBN: 0-8247-7487-6.

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()
>>> data = rng.random(size=35)
>>> res = anderson(data, dist='norm', method='interpolate')
>>> res.statistic
np.float64(0.9887620209957291)
>>> 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%.

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