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

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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1214/16-BJPS349

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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
Publisher:
Brazilian Statistical Society Publisher's website
Journal:
Brazilian Journal of Probability and Statistics Journal website
Volume:
32
Issue:
2
Pages:
437-466
Publication date:
2018-04-17
Acceptance date:
2016-12-31
DOI:
ISSN:
0103-0752
Source identifiers:
607659
Keywords:
Pubs id:
pubs:607659
UUID:
uuid:d1f88bf3-1db2-4eb4-afde-dd30528452e5
Local pid:
pubs:607659
Deposit date:
2016-03-04

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