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The Exact and Asymptotic Distributions of Cramer-von Mises Statistics

Опубликовано на портале: 06-04-2004
Journal of the Royal Statistical Society. Series B (Methodological). 1996.  Vol. 58. No. 1.
Тематический раздел:
It is shown that an asymptotically precise one-term correction to the asymptotic distribution function of the classical Cramйr-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. Abstract2 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.
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