The variance-gamma ratio distribution

Robert E. Gaunt; Siqi Li

doi:10.5802/crmath.495

Probabilités

The variance-gamma ratio distribution

Robert E. Gaunt ¹ ; Siqi Li ¹

¹ Department of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1151-1161.

Résumé

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 $X / Y$ .

Reçu le : 2023-02-24
Accepté le : 2023-03-10
Publié le : 2023-10-24

DOI : 10.5802/crmath.495

Classification : 60E05, 62E15
Mots clés : Variance-gamma distribution, ratio distribution, product of correlated normal random variables, hypergeometric function, Meijer $G$-function

Affiliations des auteurs :

Robert E. Gaunt ¹ ; Siqi Li ¹

¹ Department of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {The variance-gamma ratio distribution},
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Robert E. Gaunt; Siqi Li. The variance-gamma ratio distribution. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1151-1161. doi : 10.5802/crmath.495. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.495/

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