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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, whichinclude 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 functionof the mixed product of independent beta, gamma and central normal randomvariables.

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