A unified view on skewed distributions arising from selections

TL;DR: In this paper, a new definition of a selection distribution was proposed that encompasses many existing families of multivariate skewed distributions, such as the skew-normal and skew-elliptical distributions, and several methods of constructing selection distributions based on linear and nonlinear selection mechanisms.

Abstract: Parametric families of multivariate nonnormal distributions have received considerable attention in the past few decades. The authors propose a new definition of a selection distribution that encompasses many existing families of multivariate skewed distributions. Their work is motivated by examples that involve various forms of selection mechanisms and lead to skewed distributions. They give the main prop erties of selection distributions and show how various families of multivariate skewed distributions, such as the skew-normal and skew-elliptical distributions, arise as special cases. The authors further introduce several methods of constructing selection distributions based on linear and nonlinear selection mechanisms. Une perspective integree des lois asymetriques issues de processus de selection Resume: Les familles param6triques de lois multivari6es non gaussiennes ont suscite beaucoup d'int6ret depuis quelques decennies. Les auteurs proposent une nouvelle definition du concept de loi de selection qui englobe plusieurs familles connues de lois asymetriques multivari6es. Leurs travaux sont motives par diverses situations faisant intervenir des mecanismes de selection et conduisant 'a des lois asymetriques. Ils mentionnent les principales propri6t6s des lois de selection et montrent comment diverses familles de lois asymetriques multivariees telles que les lois asymetriques normales ou elliptiques emergent comme cas particuliers. Les auteurs presentent en outre plusieurs methodes de construction de lois de selection fondees sur des mecanismes lin6aires ou non lineaires.