A UNIFIED WEIGHTED FAMILY OF DISTRIBUTIONS WHICH CONTAINS
THE SKEW-ELLIPTICAL FAMILY
M. T. Alodat
S. O. Al-Salman
M. Y. Al-Rawwash
Abstract: In this paper, we introduce a new family of multivariate distributions, called the
unified weighted family, as a generalization to the skew-elliptical family. We study
some properties of the proposed family and show that it subsumes many important
subfamilies such as the families arisen from the selection and hidden truncation ideas.
Although the proposed family is very general, we focus on the multivariate weighted
normal family which is regarded as a promising candidate in statistical inference.
2000 AMS Mathematics Subject Classification: Primary: 62E15; Secondary:
Keywords and phrases: Multivariate weighted normal distribution, unified weighted
family of distributions, skew-elliptical family.