AndersonDarlingtests

The Anderson-Darling test is a statistical test used to determine whether a given sample of data comes from a population that follows a particular distribution. It is an extension of the Kolmogorov-Smirnov test and is particularly sensitive to differences in the tails of the distribution. The test was developed by Theodore Anderson and Donald A. Darling in 1952.

The Anderson-Darling test statistic is calculated by comparing the empirical distribution function of the sample data to the cumulative distribution function of the hypothesized distribution. The test statistic is given by:

A^2 = -n - ∑ [ (2i-1) / n * (ln(F(Xi)) + ln(1 - F(Xn+1-i))) ]

where n is the sample size, Xi are the ordered sample values, and F is the cumulative distribution function of the hypothesized distribution.

The Anderson-Darling test is often used in goodness-of-fit tests to assess whether a sample of data follows a specific distribution, such as the normal distribution. It is particularly useful when the tails of the distribution are of interest, as it gives more weight to the tails compared to the Kolmogorov-Smirnov test.

The test statistic follows a specific distribution under the null hypothesis, and critical values or p-values can be obtained from tables or statistical software to determine the significance of the test result. The Anderson-Darling test is widely used in various fields, including statistics, engineering, and finance, for hypothesis testing and model validation.