Brazilian Journal of Probability and Statistics

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

Robert E. Gaunt

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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.

Article information

Braz. J. Probab. Stat., Volume 32, Number 2 (2018), 437-466.

Received: August 2016
Accepted: December 2016
First available in Project Euclid: 17 April 2018

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Stein’s method normal distribution beta distribution gamma distribution generalised gamma distribution products of random variables distribution Meijer $G$-function


Gaunt, Robert E. Products of normal, beta and gamma random variables: Stein operators and distributional theory. Braz. J. Probab. Stat. 32 (2018), no. 2, 437--466. doi:10.1214/16-BJPS349.

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