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 financial modelling and distributional approximation on Wiener space. In this review, we provide an up-to-date account of the basic distributional theory of the VG distribution. Properties covered include probability and cumulative distribution functions, generating functions, moments and cumulants, mode and median, Stein characterisations, representations in terms of other random variables, and a list of related distributions. We also review methods for parameter estimation and some applications of the VG distribution, including the aforementioned applications to financial modelling and distributional approximation on Wiener space.

翻译：方差-伽马（VG）分布构成一个四参数分布族，其特例和极限情形包括正态分布、伽马分布和拉普拉斯分布。该分布的应用广泛，涵盖金融建模与维纳空间上的分布逼近。本文综述了VG分布的基本分布理论的最新进展，涵盖概率分布函数与累积分布函数、生成函数、矩与累积量、众数与中位数、Stein刻画、基于其他随机变量的表示形式以及相关分布列表。此外，我们还回顾了VG分布的参数估计方法及其部分应用，包括前述在金融建模与维纳空间分布逼近中的应用。