Alternative constructions of skewed multivariate distributions

A review of the construction of skewed multivariate normal distributions is presented. The review considers construction via (1) hidden truncation, (2) threshold models, (3) additive components and (4) a location and scale change for k variables beginning with k−1 independent standard normal variates and one univariate skew normal density. Extensiom to non-normal distributions have mainly used the hidden truncation approach. Unlike the normal case, the use of the three remaining techniques in constructing non-normal multivariate distributions leads to models distinct from those found using the hidden truncation approach. Examples of several tractable multivariate distributions using methods (1) and (3) are also presented.