Brazilian Journal of Probability and Statistics
- Braz. J. Probab. Stat.
- Volume 32, Number 2 (2018), 437-466.
Products of normal, beta and gamma random variables: Stein operators and distributional theory
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.
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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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