The product distribution of more-than-two correlated normal variables: A didactic review with some new findings

Haruhiko Ogasawara

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 16, 5354-5377

Abstract: Some reviews of the distribution of the product of two correlated normal random variables and the corresponding more-than-two uncorrelated cases are given with a historical perspective. The characteristic function of the product distribution of more-than-two correlated normal variables is presented using the Cholesky decomposition and an integral representation. The probability density function (pdf) of the product of these correlated variables is shown with an improper multiple integral and discussed. The pdf of the product distribution of three normal correlated variables with zero means is obtained as a mixture of the modified Bessel function of the second kind.

Date: 2025
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DOI: 10.1080/03610926.2024.2437487

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