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ELEMENTARY SYMMETRIC FUNCTIONS AND RANDOMIZATION OF $B$-DISTRIBUTIONS
Keywords:
randomization, distribution density, B-distribution, elementary symmetric functions, generalized Stirling’s numbersDOI:
https://doi.org/10.17654/0972361725042Abstract
It is known that by means of generalized Stirling’s numbers of the first kind, the distribution of any discrete random variable with a finite spectrum can be written as a so-called $B$-distribution. This article is concerned with studying the randomization of $B$-distributions by various discrete and continuous distributions, solving the inverse problem and finding specific randomizing distributions for a number of known $B$-distributions. This simple probabilistic technique replaces complex calculations and laborious analysis of $B$-distributions.
Received: February 20, 2025
Revised: March 4, 2025
Accepted: March 24, 2025
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