ELEMENTARY SYMMETRIC FUNCTIONS AND RANDOMIZATION OF -DISTRIBUTIONS

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 -distribution. This article is concerned with studying the randomization of -distributions by various discrete and continuous distributions, solving the inverse problem and finding specific randomizing distributions for a number of known -distributions. This simple probabilistic technique replaces complex calculations and laborious analysis of -distributions.