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

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

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arXiv · 2405.10178

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

Robert E. Gaunt·Saralees Nadarajah·Tibor K. Pogány

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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.

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Robert E. Gaunt, Saralees Nadarajah, Tibor K. Pogány. 2024-05-16. Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean. https://arxiv.org/abs/2405.10178

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