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

Lev Klebanov

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arXiv · 2210.01121

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

Lev Klebanov

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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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Lev Klebanov. 2022-09-30. Independence of Linear Statistics with Random Coefficients and Characterizations of Geometric and Poisson Distributions. https://arxiv.org/abs/2210.01121

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