Premium
A note on the distribution of the product of zero‐mean correlated normal random variables
Author(s) -
Gaunt Robert E.
Publication year - 2019
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12152
Subject(s) - mathematics , random variable , zero (linguistics) , probability density function , sum of normally distributed random variables , statistics , cumulative distribution function , illustration of the central limit theorem , product (mathematics) , normal distribution , variance (accounting) , combinatorics , multivariate random variable , philosophy , linguistics , geometry , accounting , business
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.