No. 175. The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis

by Mattias Villani and Rolf Larsson

Abstract: The multivariate split normal distribution extends the usual multivariate
normal distribution by a set of parameters which allows for skewness in the
form of contraction/dilation along a subset of the principal axes. This
paper derives some properties for this distribution, including its moment
generating function, multivariate skewness and kurtosis. Maximum likelihood
estimation is discussed and a complete Bayesian analysis of the multivariate
split normal model is developed.

Keywords: Bayesian inference, Elicitation, Estimation, Maximum likelihood, Multivariate analysis, Skewness.

JEL Classification: C11, C16.