Stein operators for product distributions, with applications

We build upon recent advances on the distributional aspect of Stein’s method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our results are valid for a wide class of distributions including normal, beta, variance-gamma, generalized gamma and many more. Our operators are kth degree differential operators with polynomial coefficients; they are easy to obtain even when the target density bears no explicit handle. We apply our toolkit to derive a new formula for the density of the product of k independent symmetric variance-gamma distributed random variables, and to study the asymptotic behaviour of the K-distribution under different regimes; this has implications in the analysis of radar signal data. AMS classification: 60E15, 26D10, 60B10