  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.
