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

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...

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Bibliographic Details
Published inStatistica Neerlandica Vol. 73; no. 2; pp. 176 - 179
Main Author Gaunt, Robert E.
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.05.2019
Subjects
Correlation
Mathematical analysis
Monte Carlo simulation
probability density function
Probability density functions
product of correlated normal random variables
Random variables
variance‐gamma distribution
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Summary: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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0039-0402
1467-9574
DOI:10.1111/stan.12152