scipy.stats.anderson¶
- scipy.stats.anderson(x, dist='norm')[source]¶
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’,’extreme1’}, optional
the type of distribution to test against. The default is ‘norm’ and ‘extreme1’ is a synonym for ‘gumbel’
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
[R486] http://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm [R487] Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and Some Comparisons, Journal of the American Statistical Association, Vol. 69, pp. 730-737. [R488] Stephens, M. A. (1976). Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters, Annals of Statistics, Vol. 4, pp. 357-369. [R489] Stephens, M. A. (1977). Goodness of Fit for the Extreme Value Distribution, Biometrika, Vol. 64, pp. 583-588. [R490] 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. [R491] Stephens, M. A. (1979). Tests of Fit for the Logistic Distribution Based on the Empirical Distribution Function, Biometrika, Vol. 66, pp. 591-595.