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# Anderson-Darling Test

The Anderson-Darling procedure is a general test to compare the fit of an observed cumulative distribution function to an expected cumulative distribution function. This test gives more weight to the tails than the Kolmogorov-Smirnov test.

## Definition

The Anderson-Darling statistic (A2) is defined as ## Hypothesis Testing

The null and the alternative hypotheses are:

• H0: the data follow the specified distribution;
• HA: the data do not follow the specified distribution.

The hypothesis regarding the distributional form is rejected at the chosen significance level ( ) if the test statistic, A2, is greater than the critical value obtained from a table. The fixed values of (0.01, 0.05 etc.) are generally used to evaluate the null hypothesis (H0) at various significance levels. A value of 0.05 is typically used for most applications, however, in some critical industries, a lower value may be applied.

In general, critical values of the Anderson-Darling test statistic depend on the specific distribution being tested. However, tables of critical values for many distributions (except several the most widely used ones) are not easy to find.

The Anderson-Darling test implemented in EasyFit uses the same critical values for all distributions. These values are calculated using the approximation formula, and depend on the sample size only. This kind of test (compared to the "original" A-D test) is less likely to reject the good fit, and can be successfully used to compare the goodness of fit of several fitted distributions.