A general test, published in 1952, that compares the fit of the observed cumulative distribution function with that expected. It was derived by Anderson and David A. Darling as a modification of the Cramér–von Mises test. The test statistic A2 is given by where F is the hypothesized cumulative distribution function, n is the sample size, and x(j) is the jth ordered observation (x(1)≤x(2)≤…≤x(n)). The statistic can also be used to test for normal and exponential distributions with unknown parameters estimated by their sample equivalents. In some cases, as shown in the following table, an adjusted test statistic is required.
upper tail probability
Normal, estimated mean (n>20)
Normal, estimated variance (n>20)
Normal, estimated mean and variance
Exponential, estimated mean
Subjects: Probability and Statistics.