Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean∗

Robert E. Gaunt; Saraleesan Nadarajah; Tibor K. Pogány

doi:10.1016/j.jmaa.2025.129800

Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean∗

University of Rijeka
Obuda University

Research output: Contribution to journal › Article › peer-review

10 Downloads (Pure)

Abstract

We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of independent copies of such random variables.

Original language	English
Journal	Journal of Mathematical Analysis and Applications
DOIs	https://doi.org/10.1016/j.jmaa.2025.129800
Publication status	Published - 1 Dec 2025

Keywords

Product of correlated normal random variables
infinite divisibility
sum of independent random variables
probability density function
confluent hypergeometric function
modified Bessel function.

Access to Document

10.1016/j.jmaa.2025.129800Licence: CC BY

1-s2.0-S0022247X25005815-mainFinal published version, 686 KBLicence: CC BY

1 Finished
1 Active

Rates of Convergence in Multivariate Normal Approximation by Stein's Method
Gaunt, R. (PI)
1/03/24 → 28/02/27
Project: Research
Berry-Esseen bounds for the stable central limit theorem by Stein's method
Gaunt, R. (PI)
1/10/24 → 30/09/25
Project: Research

Cite this

@article{5c91bf96d80348cab76d2f8a6f59742c,

title = "Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean∗",

abstract = "We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of independent copies of such random variables.",

keywords = "Product of correlated normal random variables, infinite divisibility, sum of independent random variables, probability density function, confluent hypergeometric function, modified Bessel function.",

author = "Gaunt, \{Robert E.\} and Saraleesan Nadarajah and Pog{\'a}ny, \{Tibor K.\}",

year = "2025",

month = dec,

day = "1",

doi = "10.1016/j.jmaa.2025.129800",

language = "English",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean∗

AU - Gaunt, Robert E.

AU - Nadarajah, Saraleesan

AU - Pogány, Tibor K.

PY - 2025/12/1

Y1 - 2025/12/1

N2 - We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of independent copies of such random variables.

AB - We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of independent copies of such random variables.

KW - Product of correlated normal random variables

KW - infinite divisibility

KW - sum of independent random variables

KW - probability density function

KW - confluent hypergeometric function

KW - modified Bessel function.

U2 - 10.1016/j.jmaa.2025.129800

DO - 10.1016/j.jmaa.2025.129800

M3 - Article

SN - 0022-247X

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

ER -

Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean∗

Abstract

Keywords

Access to Document

Fingerprint

Projects

Rates of Convergence in Multivariate Normal Approximation by Stein's Method

Berry-Esseen bounds for the stable central limit theorem by Stein's method

Cite this