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

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    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.
    Original languageEnglish
    Pages (from-to)176-179
    JournalStatistica Neerlandica
    Volume73
    Early online date25 Jul 2018
    DOIs
    Publication statusPublished - May 2019

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