Some properties of skew-symmetric distributions

TL;DR

This paper investigates the general properties of skew-symmetric distributions, establishing conditions on their components to ensure specific distributional characteristics, thus broadening understanding beyond specific sub-families.

Contribution

It provides general conditions on the components of skew-symmetric distributions to guarantee certain properties, extending the theoretical understanding of this broad family.

Findings

Conditions for skew-symmetric distributions to have desired properties

General framework applicable to various sub-families

Enhanced understanding of distributional characteristics

Abstract

The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense recent work has produced several results for specific sub-families of this construction, but much less is known in general terms. The present paper explores some questions within this framework, and provides conditions on the above-mentioned components to ensure that the final distribution enjoys specific properties.