  Parametric distributions are an important part of statistics. There is now a
voluminous literature on different fascinating formulations of flexible
distributions. We present a selective and brief overview of a small subset of
these distributions, focusing on those that are obtained by scaling the mean
and/or covariance matrix of the (multivariate) normal distribution with some
scaling variable(s). Namely, we consider the families of mean mixture, variance
mixture, and mean-variance mixture of normal distributions. Its basic
properties, some notable special/limiting cases, and parameter estimation
methods are also described.
