The Exact and Asymptotic Distributions of Cramer-von Mises Statistics

It is shown that an asymptotically precise one-term correction to the asymptotic distribution function of the classical Cramer-von Mises statistic approximates the exact distribution function remarkably closely for sample sizes as small as 7 or even smaller. This correction can be quickly evaluated,...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1996-01, Vol.58 (1), p.221-234
Main Authors: Csorgo, Sandor, Faraway, Julian J.
Format: Article
Language:English
Subjects:
Approximation
asymptotic expansions
cramér‐von mises statistic
Decimals
Distribution
Distribution functions
Exact sciences and technology
Mathematical functions
Mathematics
Nonparametric inference
Numerical integration
P values
Probability and statistics
Sample size
Samples
Sampling distributions
Sciences and techniques of general use
small sample distributions
Statistics
watson's statistic
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Summary:It is shown that an asymptotically precise one-term correction to the asymptotic distribution function of the classical Cramer-von Mises statistic approximates the exact distribution function remarkably closely for sample sizes as small as 7 or even smaller. This correction can be quickly evaluated, and hence it is suitable for the computation of practically exact p-values when testing simple goodness of fit. Similar findings hold for Watson's rotationally invariant modification, where a sample size of 4 appears to suffice.
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1996.tb02077.x