Products of normal, beta and gamma random variables: Stein operators and distributional theory

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Abstract

In this paper, we extend Stein’s method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein operators for mixed products of these distributions, which include the classical beta, gamma and normal Stein operators as special cases. These operators lead us to closed-form expressions involving the Meijer G-function for the probability density function and characteristic function of the mixed product of independent beta, gamma and central normal random variables.

Bibliographical metadata

Original languageEnglish
Pages (from-to)437-466
JournalBrazilian Journal of Probability and Statistics
Volume32
Issue number2
DOIs
StatePublished - 17 Apr 2018