## Brazilian Journal of Probability and Statistics

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

Robert E. Gaunt

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.bjps/1523952022

Digital Object Identifier
doi:10.1214/16-BJPS349

Mathematical Reviews number (MathSciNet)
MR3787761

Zentralblatt MATH identifier
06914682

#### Citation

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. https://projecteuclid.org/euclid.bjps/1523952022

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