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Stein’s method and the distribution of the product of zero mean correlated normal random variables

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  • Robert E. Gaunt

Abstract

Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a recent technique from the Stein’s method literature to obtain a simple new proof, which also serves as an exposition of a general method that may be useful in related problems.

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  • Robert E. Gaunt, 2021. "Stein’s method and the distribution of the product of zero mean correlated normal random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(2), pages 280-285, January.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:2:p:280-285
    DOI: 10.1080/03610926.2019.1634210
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    Cited by:

    1. Antonio Seijas-Macias & Amílcar Oliveira & Teresa A. Oliveira, 2023. "A New R-Function to Estimate the PDF of the Product of Two Uncorrelated Normal Variables," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    2. Robert E. Gaunt, 2022. "The basic distributional theory for the product of zero mean correlated normal random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 450-470, November.

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