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 bywhere 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 distribution and exponential distribution with unknown parameters estimated by their sample equivalents. In some cases, as shown in the following table, an adjusted test statistic is required.