Approximating the tail of the Anderson–Darling distribution

The Anderson–Darling distribution plays an important role in the statistical testing of uniformity. However, it is difficult to evaluate, especially in its tail. We consider a new Monte Carlo approach to approximate the tail probabilities of the Anderson–Darling distribution. The estimates are compared with existing tables and recent numerical approximations, obtained via numerical inversion and naive Monte Carlo. Our results demonstrate improved accuracy over existing tables and approximating functions for small tail probabilities. We also present an approximating function for tail probabilities of less than 3×10−2.