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December, 1967 Distributions of a M. Kac Statistic
J. L. Allen, J. A. Beekman
Ann. Math. Statist. 38(6): 1919-1923 (December, 1967). DOI: 10.1214/aoms/1177698629


In 1949, M. Kac defined a statistic which appears useful for statistical problems arising in insurance, biology, and telephone engineering [2]. In those fields, the natural observation period is a fixed time period during which a random number of observations would be obtained. The distribution of the number of observations is given by a Poisson distribution. Distributions of this statistic can be used to determine upper and lower confidence contours for an unknown distribution, or in testing a distribution hypothesis. The purpose of this note is to extend the authors' earlier results, [1], to the two-sided Kac statistic.


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J. L. Allen. J. A. Beekman. "Distributions of a M. Kac Statistic." Ann. Math. Statist. 38 (6) 1919 - 1923, December, 1967.


Published: December, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0183.21701
MathSciNet: MR217911
Digital Object Identifier: 10.1214/aoms/1177698629

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 6 • December, 1967
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