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 re- sult 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.