Open AccessAlternative constructions of skewed multivariate distributions
Author(s) -
Barry C. Arnold,
Robert J. Beaver
Publication year - 2004
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2004.08.03
Subject(s) - multivariate statistics , truncation (statistics) , univariate , skew normal distribution , mathematics , skew , multivariate normal distribution , multivariate analysis , statistics , truncated normal distribution , normal distribution , econometrics , computer science , telecommunications
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.