Distributions of a M. Kac Statistic

Abstract

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.