The variance-gamma ratio distribution
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including identification of parameter regimes under which the density is boun...
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Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.495/ |
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| author | Gaunt, Robert E. Li, Siqi |
| author_facet | Gaunt, Robert E. Li, Siqi |
| author_sort | Gaunt, Robert E. |
| collection | DOAJ |
| description | Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including identification of parameter regimes under which the density is bounded, asymptotic approximations of tail probabilities, and fractional moments; in particular, we see that the mean is undefined. In the case that $X$ and $Y$ are independent symmetric variance-gamma random variables, an exact formula is also given for the cumulative distribution function of the ratio $X/Y$. |
| format | Article |
| id | doaj-art-49236110ec294a618deea601e97a5cf5 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-49236110ec294a618deea601e97a5cf52025-02-07T11:09:55ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G71151116110.5802/crmath.49510.5802/crmath.495The variance-gamma ratio distributionGaunt, Robert E.0Li, Siqi1Department of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UKDepartment of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UKLet $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including identification of parameter regimes under which the density is bounded, asymptotic approximations of tail probabilities, and fractional moments; in particular, we see that the mean is undefined. In the case that $X$ and $Y$ are independent symmetric variance-gamma random variables, an exact formula is also given for the cumulative distribution function of the ratio $X/Y$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.495/Variance-gamma distributionratio distributionproduct of correlated normal random variableshypergeometric functionMeijer $G$-function |
| spellingShingle | Gaunt, Robert E. Li, Siqi The variance-gamma ratio distribution Comptes Rendus. Mathématique Variance-gamma distribution ratio distribution product of correlated normal random variables hypergeometric function Meijer $G$-function |
| title | The variance-gamma ratio distribution |
| title_full | The variance-gamma ratio distribution |
| title_fullStr | The variance-gamma ratio distribution |
| title_full_unstemmed | The variance-gamma ratio distribution |
| title_short | The variance-gamma ratio distribution |
| title_sort | variance gamma ratio distribution |
| topic | Variance-gamma distribution ratio distribution product of correlated normal random variables hypergeometric function Meijer $G$-function |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.495/ |
| work_keys_str_mv | AT gauntroberte thevariancegammaratiodistribution AT lisiqi thevariancegammaratiodistribution AT gauntroberte variancegammaratiodistribution AT lisiqi variancegammaratiodistribution |