Independence of Linear Statistics with Random Coefficients and Characterizations of Geometric and Poisson Distributions

Abstract

There is given a characterization of the geometric distribution by the independence of linear forms with random coefficients. The result is a discrete analog of the corresponding theorem on exponential distribution. The property of linear statistics independence is also a characterization of Poisson law. Keywords: geometric distribution; exponential distribution; Poisson distribution; linear forms; random coefficients

5 pages, no figures