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

Journal article

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.

Files:: ngb prods jotp.pdf

(Preview, Accepted manuscript, pdf, 345.5KB, Terms of use)

Institution:

University of Oxford

Division:

MPLS

Department:

Statistics

Role:

Author

Publisher:: Brazilian Statistical Society
Journal:: Brazilian Journal of Probability and Statistics More from this journal
Volume:: 32
Issue:: 2
Pages:: 437-466
Publication date:: 2018-04-17
Acceptance date:: 2016-12-31
DOI:: 10.1214/16-BJPS349
ISSN:: 0103-0752

Keywords:: beta distribution

gamma distribution

Meijer G-function

products of random variables

generalised gamma distribution

Stein's method

normal distribution
Pubs id:: pubs:607659
UUID:: uuid:d1f88bf3-1db2-4eb4-afde-dd30528452e5
Local pid:: pubs:607659
Source identifiers:: 607659
Deposit date:: 2016-03-04

Notes:: This is the accepted manuscript version of the article. The final version is available online from Brazilian Statistical Society at: 10.1214/16-BJPS349

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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