Approximating the tail of the Anderson–Darling distribution

Adam W. Grace and Ian A. Wood

Computational Statistics & Data Analysis, 2012, vol. 56, issue 12, 4301-4311

Abstract: 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.

Keywords: Anderson–Darling distribution; Rare-event estimation; Generalized splitting; Hit-and-run sampler; Approximating function (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:12:p:4301-4311

DOI: 10.1016/j.csda.2012.04.002

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