Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 2, 206--226

CONDITIONALLY SPECIFIED MULTIVARIATE SKEWED DISTRIBUTIONS

By

BARRY C. ARNOLD, University of California, Riverside, USA

ENRIQUE CASTILLO

and

JOS\'E MAR\'IA SARABIA, University of Cantabria, Santander, Spain

SUMMARY. The basic skew normal model $f(x;\lambda)= 2\phi(x)\Phi(\lambda x)$, where $\phi$ (respectively $\Phi$) is the standard normal density (respectively distribution), may be used as a component in the construction of flexible families of multivariate densities using a conditional specification paradigm. Parallel developments are outlined in the case in which the basic distribution is something other than normal (for example, Cauchy). The development of these and related models involves identification of broad classes of particular solutions to certain functional equations.

*AMS (1991) subject classification}. *Primary 62H05.

*Key words and phrases. *Skewed normal density, hidden truncation, functional equations, Cauchy, Laplace, logistic, normal conditionals.