文章基本信息

标题：Products of normal, beta and gamma random variables: Stein operators and distributional theory
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作者：Robert E. Gaunt
期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2018
卷号：32
期号：2
页码：437-466
DOI：10.1214/16-BJPS349
语种：English
出版社：Brazilian Statistical Association
摘要：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.