Scandinavian Working Papers in Economics

Working Paper Series,
Sveriges Riksbank (Central Bank of Sweden)

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

Mattias Villani () and Rolf Larsson
Additional contact information
Mattias Villani: Research Department, Central Bank of Sweden, Postal: Sveriges Riksbank, SE-103 37 Stockholm, Sweden
Rolf Larsson: Department of Information Science, Uppsala University, Postal: Box 513, SE-751 20 Uppsala, Sweden

Abstract: The multivariate split nomal 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 prinicpal axis. The 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 distribution is developed.

Keywords: Bayesian inference; Elicitation; Estimation; Maximum likelihood; Multivariate analysis; Skewness

JEL-codes: C11; C16

25 pages, December 1, 2004

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