Asymptotic expansions relating to the distribution of the product of correlated normal random variables
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915302454853632 |
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| author | Gaunt, Robert E. Ye, Zixin |
| author_facet | Gaunt, Robert E. Ye, Zixin |
| contents | Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables. Asymptotic approximations are also given for the quantile function. Numerical results are given to test the performance of the asymptotic approximations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_03942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic expansions relating to the distribution of the product of correlated normal random variables Gaunt, Robert E. Ye, Zixin Probability Classical Analysis and ODEs Primary 41A60, 60E05, 62E15 Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables. Asymptotic approximations are also given for the quantile function. Numerical results are given to test the performance of the asymptotic approximations. |
| title | Asymptotic expansions relating to the distribution of the product of correlated normal random variables |
| topic | Probability Classical Analysis and ODEs Primary 41A60, 60E05, 62E15 |
| url | https://arxiv.org/abs/2411.03942 |