Alternative constructions of skewed multivariate distributions

  • Barry C. Arnold University of California
  • Robert J. Beaver University of California
Keywords: skewed distributions, hidden truncation, additive components


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.


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