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The Anderson-Darling test

It is a statistical test used to test whether a sample of data comes from a particular theoretical distribution. Unlike the Kolmogorov-Smirnov test, the Anderson-Darling test assigns greater weights to the tails of the distribution, making it more sensitive to discrepancies in these areas.

How to Interpret It?

Null Hypothesis (H0): the data comes from the specified theoretical distribution.

Alternative Hypothesis (H1): the data does not come from the specified theoretical distribution.

The empirical and theoretical cumulative distributions above, and below a U shaped curve of the weight the Anderson-Darling test gives to each gap: low in the center, high in both tails.
Anderson-Darling weights the tails more than Kolmogorov-Smirnov, so it notices errors where extreme events live.

The test calculates a test statistic (Aˆ2) that measures the discrepancy between the empirical distribution function of the data and the expected theoretical distribution.

Critical values and significance: these values are used to compare the calculated AΒ² statistic with a critical value corresponding to a given level of significance.

If the AΒ² statistic is greater than the critical value, the null hypothesis is rejected.

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