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

2022/09/30 by Klebanov, Lev
#60E05 #60E10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2210.01121

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

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