A Stein characterisation of the distribution of the product of correlated normal random variables

Robert E. Gaunt, Siqi Li and Heather L. Sutcliffe

Statistics & Probability Letters, 2025, vol. 216, issue C

Abstract: We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein characterisation is shown to naturally generalise a number of other Stein characterisations in the literature. From our Stein characterisation we derive recursive formulas for the moments of the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, which allows for efficient computation of higher order moments.

Keywords: Product of correlated normal random variables; Stein characterisation; Stein’s method; Moments (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110269

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