Anderson-Darling test

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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.

See also

• Kolmogorov-Smirnov test
• Shapiro-Wilk test
• Smirnov-Cramer-Von-Mises test

External links

US NIST Handbook of Statistics