Geodesic
Probabilités
The variance-gamma ratio distribution
Gaunt, Robert E.1  ; Li, Siqi1
1 Department of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
Comptes Rendus. Mathématique, Tome 361 (2023) no. G7, pp. 1151-1161

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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.

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DOI : 10.5802/crmath.495
Classification : 60E05, 62E15
Keywords: Variance-gamma distribution, ratio distribution, product of correlated normal random variables, hypergeometric function, Meijer $G$-function

Gaunt, Robert E. 1 ; Li, Siqi 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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Gaunt, Robert E.; Li, Siqi. The variance-gamma ratio distribution. Comptes Rendus. Mathématique, Tome 361 (2023) no. G7, pp. 1151-1161. doi: 10.5802/crmath.495

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