Approximating the tail of the Anderson–Darling distribution

Grace, Adam W. and Wood, Ian A. (2012) Approximating the tail of the Anderson–Darling distribution. Computational Statistics and Data Analysis, 56 12: 4301-4311. doi:10.1016/j.csda.2012.04.002

Author Grace, Adam W.
Wood, Ian A.
Title Approximating the tail of the Anderson–Darling distribution
Journal name Computational Statistics and Data Analysis   Check publisher's open access policy
ISSN 0167-9473
Publication date 2012
Sub-type Article (original research)
DOI 10.1016/j.csda.2012.04.002
Volume 56
Issue 12
Start page 4301
End page 4311
Total pages 11
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Collection year 2013
Language eng
Formatted 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.
Keyword Anderson–Darling distribution
Rare-event estimation
Generalized splitting
Hit-and-run sampler
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Available online 11 April 2012

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
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Citation counts: TR Web of Science Citation Count  Cited 4 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 12 times in Scopus Article | Citations
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Created: Mon, 16 Apr 2012, 15:46:12 EST by Mr Ian Wood on behalf of Mathematics