Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913883730477056 |
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| author | Gaunt, Robert E. Nadarajah, Saralees Pogány, Tibor K. |
| author_facet | Gaunt, Robert E. Nadarajah, Saralees Pogány, Tibor K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean Gaunt, Robert E. Nadarajah, Saralees Pogány, Tibor K. Probability Primary 60E05, 60E07, 62E15, Secondary 33C15, 60E10 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. |
| title | Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean |
| topic | Probability Primary 60E05, 60E07, 62E15, Secondary 33C15, 60E10 |
| url | https://arxiv.org/abs/2405.10178 |