Order Statistics in Goodness-of-Fit Testing

A new method is presented for using order statistics to judge the fit of a distribution to data. A test statistic based on quantiles of order statistics compares favorably with the Kolmogorov–Smirnov and Anderson–Darling test statistics. The performance of the new goodness-of-fit test statistic is e...

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Bibliographic Details
Published inComputational Probability Applications Vol. 247; pp. 31 - 39
Main Authors Glen, Andrew G., Barr, Donald R., Leemis, Lawrence M.
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2017
Springer International Publishing
SeriesInternational Series in Operations Research & Management Science
Subjects
Computational algebra system
Goodness-of-fit
Mathematical & statistical software
Model adequacy
Operational research
Order statistics
Power
Probability & statistics
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ISBN3319433156
9783319433158
ISSN0884-8289
2214-7934
DOI10.1007/978-3-319-43317-2_3

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Summary:A new method is presented for using order statistics to judge the fit of a distribution to data. A test statistic based on quantiles of order statistics compares favorably with the Kolmogorov–Smirnov and Anderson–Darling test statistics. The performance of the new goodness-of-fit test statistic is examined with simulation experiments. For certain hypothesis tests, the test statistic is more powerful than the Kolmogorov–Smirnov and Anderson–Darling test statistics. The new test statistic is calculated using a computer algebra system because of the need to compute exact distributions of order statistics.
Bibliography:Originally published in IEEE Transactions on Reliability, Volume 50, Number 2 in 2001, this paper is the first result using APPL to improve goodness of fit testing. Because many tests rely on the probability integral transform which makes many tests reduce to uniformity tests, APPL’s Transform procedure, used with OrderStat, produces exact distributions of random PDFs of order statistics. This means that new distributions are created during the calculation of the actual test statistic. This type of creation of new distributions is not possible in standard statistical packages.
ISBN:3319433156
9783319433158
ISSN:0884-8289
2214-7934
DOI:10.1007/978-3-319-43317-2_3