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Stein's method and the distribution of the product of zero mean correlated normal random variables [PDF]

Communications in Statistics - Theory and Methods, 2019
Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a recent technique from the Stein's method literature to obtain a simple new proof, which also serves as an exposition ...
Robert E. Gaunt
semanticscholar   +14 more sources

A Stein characterisation of the distribution of the product of correlated normal random variables [PDF]

Statistics & Probability Letters
We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein characterisation is shown to naturally generalise a number of other Stein characterisations in the literature.
Robert E. Gaunt, Siqi Li, H Sutcliffe
semanticscholar   +7 more sources

Asymptotic approximations for the distribution of the product of correlated normal random variables [PDF]

Journal of Mathematical Analysis and Applications, 2023
20 ...
Robert E. Gaunt, Zixin Ye
semanticscholar   +5 more sources

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

Statistica Neerlandica, 2018
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 ...
Robert E. Gaunt
semanticscholar   +10 more sources

The basic distributional theory for the product of zero mean correlated normal random variables [PDF]

Statistica Neerlandica, 2022
AbstractThe product of two zero mean correlated normal random variables, and more generally the sum of independent copies of such random variables, has received much attention in the statistics literature and appears in many application areas. However, many important distributional properties are yet to be recorded.
Robert E. Gaunt
semanticscholar   +6 more sources

On the distribution of the product of correlated normal random variables

Comptes Rendus. Mathématique, 2015
We solve a problem that has remained unsolved since 1936 – the exact distribution of the product of two correlated normal random variables. As a by-product, we derive the exact distribution of the mean of the product of correlated normal random variables.
Saralees Nadarajah, Tibor K. Pogány
semanticscholar   +5 more sources

Asymptotic approximations for the distribution of the product of correlated normal random variables

, 2023
We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances.
Robert E. Gaunt, Zixin Ye
openalex   +4 more sources

Asymptotic expansions for the distribution of the product of correlated normal random variables [PDF]

22 pages.
Robert E. Gaunt, Zixin Ye
openalex   +3 more sources

Note on the moment generating function of the multivariate normal distribution

Miskolc Mathematical Notes
We present a streamlined proof of a formula for the derivatives of the moment generating function of the multivariate normal distribution. We formulate it in terms of the summation of the contractions by pairings, which encodes a combinatorial ...
Kenichi Hirose
doaj   +2 more sources

Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean [PDF]

15 ...
Robert E. Gaunt, Saralees Nadarajah, Tibor K. Pogány   +2 more
openalex   +3 more sources