scipy.stats.anderson

scipy.stats.anderson(x, dist='norm')

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, or Gumbel (Extreme Value Type I) distributions.

Parameters

xarray_like

Array of sample data.

dist{‘norm’, ‘expon’, ‘logistic’, ‘gumbel’, ‘gumbel_l’, ‘gumbel_r’,

‘extreme1’}, 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.

Returns

statisticfloat

The Anderson-Darling test statistic.

critical_valueslist

The critical values for this distribution.

significance_levellist

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.

See also

kstest

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

Notes

Critical values provided are for the following significance levels:

normal/exponenential

15%, 10%, 5%, 2.5%, 1%

logistic

25%, 10%, 5%, 2.5%, 1%, 0.5%

Gumbel

25%, 10%, 5%, 2.5%, 1%

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.

References

1

https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm

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.