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A note on the distribution of the product of zero‐mean correlated normal random variables

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  • Robert E. Gaunt

Abstract

The problem of finding an explicit formula for the probability density function of two zero‐mean correlated normal random variables dates back to 1936. Perhaps, surprisingly, this problem was not resolved until 2016. This is all the more surprising given that a very simple proof is available, which is the subject of this note; we identify the product of two zero‐mean correlated normal random variables as a variance‐gamma random variable, from which an explicit formula for the probability density function is immediate.

Suggested Citation

  • Robert E. Gaunt, 2019. "A note on the distribution of the product of zero‐mean correlated normal random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 73(2), pages 176-179, May.
    • Handle: RePEc:bla:stanee:v:73:y:2019:i:2:p:176-179
    DOI: 10.1111/stan.12152
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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. Saulius Jokubaitis & Remigijus Leipus, 2022. "Asymptotic Normality in Linear Regression with Approximately Sparse Structure," Mathematics, MDPI, vol. 10(10), pages 1-28, May.
    3. Beaulieu Guillaume Boglioni & de Micheaux Pierre Lafaye & Ouimet Frédéric, 2021. "Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin," Dependence Modeling, De Gruyter, vol. 9(1), pages 424-438, January.

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