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Biometrika 1970 57(3):661-664; doi:10.1093/biomet/57.3.661
© 1970 by Biometrika Trust
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On the conditional moments of the k-statistics for the Poisson distribution

JOHN J. GART and HUGH M. PETTIGREW

National Cancer Institute Bethesda, Maryland

SUMMARY

Consider a random sample, x1, ..., xn, from a Poisson distribution. The Rao-Blackwell theorem and the completeness property of this distribution are exploited to show that E(kj\{sigma}xi = X) = x¯ (i = 1, 2, ...) and to find higher conditional moments of the sample cumulants. Some possible applications to the testing of the fit of the Poisson distribution are suggested.


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