scipy.stats.anderson

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

Anderson-Darling test for data coming from a particular distribution

The Anderson-Darling test is a modification of the Kolmogorov- Smirnov test kstest for 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:

x : array_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’ and ‘extreme1’, ‘gumbel_l’ and ‘gumbel’ are synonyms.

Returns:

statistic : float

The Anderson-Darling test statistic

critical_values : list

The critical values for this distribution

significance_level : list

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.

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 A2 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.

References

[R601]

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

[R602]

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

[R603]

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

[R604]

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

[R605]

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.

[R606]

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