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Approximating the tail of the Anderson–Darling distribution

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  • Grace, Adam W.
  • Wood, Ian A.

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.

Suggested Citation

  • Grace, Adam W. & Wood, Ian A., 2012. "Approximating the tail of the Anderson–Darling distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4301-4311.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4301-4311
    DOI: 10.1016/j.csda.2012.04.002
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    References listed on IDEAS

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    1. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    2. Marsaglia, George & Marsaglia, John, 2004. "Evaluating the Anderson-Darling Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i02).
    3. Pierre L'Écuyer & Jean-François Cordeau & Richard Simard, 2000. "Close-Point Spatial Tests and Their Application to Random Number Generators," Operations Research, INFORMS, vol. 48(2), pages 308-317, April.
    4. Gregory Camilli, 1995. "The relationship between Fisher's exact test and Pearson's chi-square test: A bayesian perspective," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 305-312, June.
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