Journal
BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS
Volume 32, Issue 2, Pages 437-466Publisher
BRAZILIAN STATISTICAL ASSOCIATION
DOI: 10.1214/16-BJPS349
Keywords
Stein's method; normal distribution; beta distribution; gamma distribution; generalised gamma distribution; products of random variables distribution; Meijer G-function
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Funding
- EPSRC grant [EP/K032402/1]
- Dame Kathleen Ollerenshaw Research Fellowship
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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.
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