The Exact and Asymptotic Distributions of Cramér-Von Mises Statistics

Sándor CSöRgő; Julian J. Faraway

doi:10.1111/j.2517-6161.1996.tb02077.x

The Exact and Asymptotic Distributions of Cramér-Von Mises Statistics

Sándor CSöRgő, Julian J. Faraway

University of Michigan

Research output: Contribution to journal › Article › peer-review

104 Citations (SciVal)

Abstract

It is shown that an asymptotically precise one-term correction to the asymptotic distribution function of the classical Cramér-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.

Original language	English
Pages (from-to)	221-234
Number of pages	14
Journal	Journal of the Royal Statistical Society. Series B: Methodological
Volume	58
Issue number	1
DOIs	https://doi.org/10.1111/j.2517-6161.1996.tb02077.x
Publication status	Published - 1 Jan 1996

Keywords

asymptotic expansions
cramér-von mises statistic
small sample distributions
watson's statistic

ASJC Scopus subject areas

Statistics and Probability

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10.1111/j.2517-6161.1996.tb02077.x

Cite this

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The Exact and Asymptotic Distributions of Cramér-Von Mises Statistics

Abstract

Keywords

ASJC Scopus subject areas

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