Selection models under generalized symmetry settings

TL;DR

This paper explores new applications of a general lemma related to skew-elliptical densities, extending beyond traditional skew-symmetric distributions, and introduces novel probability distributions within this framework.

Contribution

It demonstrates broader applicability of the lemma and constructs new probability distributions outside the skew-symmetric family.

Findings

Broader applicability of the lemma to skew-elliptical densities

Construction of new probability distributions outside skew-symmetric densities

Extension of existing models to generalized symmetry settings

Abstract

An active stream of literature has followed up the idea of skew-elliptical densities initiated by Azzalini and Capitanio (1999). Their original formulation was based on a general lemma which is however of broader applicability than usually perceived. This note examines new directions of its use, and illustrates them with the construction of some probability distributions falling outside the family of the so-called skew-symmetric densities.