Anderson-Darling test

The Anderson-Darling test assesses whether known data come from a specified distribution. The formula for the test statistic $$A$$ to assess if data $$\{Y_1<\dots <Y_N\}$$ (note that the data must be put in order) comes from a distribution with cumulative distribution function $$F$$ is

$$A^2 = -N-S$$

where

$$S=\sum_{i=1}^N \frac{2i-1}{N}\left[\ln F(Y_i) + \ln\left(1-F(Y_{N+1-i})\right)\right]$$

The test statistic can then be compared against the distributions of the test statistic (dependent on which $$F$$ is used) to determine the P-value.