The Variance-Gamma Distribution: A Review

Journal article

The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financialmodelling and distributional approximation on Wiener space. In this review,we provide an up-to-date account of the basic distributional theory of theVG distribution. Properties covered include probability and cumulative distribution functions, generating functions, moments and cumulants, mode and median, Stein characterisations, representations in terms of other randomvariables, and a list of related distributions. We also review methods for parameter estimation and some applications of the VG distribution, includingthe aforementioned applications to financial modelling and distributional approximation on Wiener space

Authors: Fischer, A; Gaunt, RE; Sarantsev, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Institute of Mathematical Statistics
• Journal: Statistical Science
• Volume: 40
• Issue: 2
• Pages: 235-258
• Publication date: 2025-05-01
• DOI: 10.1214/24-sts929
• EISSN: 2168-8745
• ISSN: 0883-4237
• Language: English
• Keywords: Econometrics; Computer science; Distribution (mathematics); Gamma distribution; Statistics; Economics; Mathematics; Variance (accounting)