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October, 1966 A Statistical Test Involving a Random Number of Random Variables
J. L. Allen, J. A. Beekman
Ann. Math. Statist. 37(5): 1305-1311 (October, 1966). DOI: 10.1214/aoms/1177699274


In this paper is studied a technique based on samples of the form $N, X_1, X_2, \cdots, X_N$ where $N$ has a Poisson distribution, and each $X_i$ has the same continuous distribution function. Such samples, rather than fixed number samples, are appropriate for fixed time period observations where the number of occurrences is a Poisson variate, and are used in biology, insurance, and telephone engineering. We shall introduce a one-sided Kac statistic which is similar to the one-sided Kolmogorov statistic, derive forms for its finite dimensional and asymptotic distributions, find a lower bound for the power of the test, and prove that the test is "modified" consistent. Tabulations of the distributions will be given.


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J. L. Allen. J. A. Beekman. "A Statistical Test Involving a Random Number of Random Variables." Ann. Math. Statist. 37 (5) 1305 - 1311, October, 1966.


Published: October, 1966
First available in Project Euclid: 27 April 2007

zbMATH: 0149.15004
MathSciNet: MR198619
Digital Object Identifier: 10.1214/aoms/1177699274

Rights: Copyright © 1966 Institute of Mathematical Statistics

Vol.37 • No. 5 • October, 1966
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