Infinite divisibility of the product of two correlated normal random variables and exact distribution of the sample mean
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.
Authors
- Saralees Nadarajah (ORCID: https://orcid.org/0000-0002-0481-0372)
- Robert E. Gaunt (ORCID: https://orcid.org/0000-0001-6187-0657)
- Tibor K. Pogány (ORCID: https://orcid.org/0000-0002-4635-8257)
Publication Details
- Journal
- Journal of Mathematical Analysis and Applications
- Published
- 2025-06-16
- DOI
- https://doi.org/10.1016/j.jmaa.2025.129800
- Citations
- 3
- Primary Topic
- Statistical Distribution Estimation and Applications
- Type
- article
- Field-Weighted Citation Impact
- 7.89
Funders
- Engineering and Physical Sciences Research Council