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arXiv:2405.10178 [math.PR]AbstractReferencesReviewsResources

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

Published 2024-05-16Version 1

We prove that the distribution of the product of two correlated normal random variables with non-zero 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.

Comments: 15 pages
Categories: math.PR
Subjects: 60E05, 60E07, 62E15, 33C15, 60E10
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