Evaluating the Anderson-Darling Distribution

Evaluating the Anderson-Darling Distribution

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Except for n = 1, only the limit as n approaches infinity for the distribution of the Anderson-Darling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation m...

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Main Authors: George Marsaglia, John Marsaglia
Format: Article
Language:English
Published: Foundation for Open Access Statistics 2004-02-01
Series:Journal of Statistical Software
Online Access:http://www.jstatsoft.org/index.php/jss/article/view/2321
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spelling doaj-28d8aa763da847618c0b35a5a1b92af52020-11-25T00:15:34ZengFoundation for Open Access StatisticsJournal of Statistical Software1548-76602004-02-01911510.18637/jss.v009.i02925Evaluating the Anderson-Darling DistributionGeorge MarsagliaJohn MarsagliaExcept for n = 1, only the limit as n approaches infinity for the distribution of the Anderson-Darling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation methods. We give here our method for evaluating that asymptotic distribution to great accuracy--directly, via series with two-term recursions. We also give, for any particular n, a procedure for evaluating the distribution to the fourth digit, based on empirical CDF's from samples of size 1010 .http://www.jstatsoft.org/index.php/jss/article/view/2321
collection DOAJ
language English
format Article
sources DOAJ
author George Marsaglia
John Marsaglia
spellingShingle George Marsaglia
John Marsaglia
Evaluating the Anderson-Darling Distribution
Journal of Statistical Software
author_facet George Marsaglia
John Marsaglia
author_sort George Marsaglia
title Evaluating the Anderson-Darling Distribution
title_short Evaluating the Anderson-Darling Distribution
title_full Evaluating the Anderson-Darling Distribution
title_fullStr Evaluating the Anderson-Darling Distribution
title_full_unstemmed Evaluating the Anderson-Darling Distribution
title_sort evaluating the anderson-darling distribution
publisher Foundation for Open Access Statistics
series Journal of Statistical Software
issn 1548-7660
publishDate 2004-02-01
description Except for n = 1, only the limit as n approaches infinity for the distribution of the Anderson-Darling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation methods. We give here our method for evaluating that asymptotic distribution to great accuracy--directly, via series with two-term recursions. We also give, for any particular n, a procedure for evaluating the distribution to the fourth digit, based on empirical CDF's from samples of size 1010 .
url http://www.jstatsoft.org/index.php/jss/article/view/2321
work_keys_str_mv AT georgemarsaglia evaluatingtheandersondarlingdistribution
AT johnmarsaglia evaluatingtheandersondarlingdistribution
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