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