Identifiability of two-component skew normal mixtures with one known component

TL;DR

This paper establishes conditions under which the mixing proportions in two-component skew normal mixture models can be uniquely identified, including univariate and multivariate cases with known components.

Contribution

It provides new sufficient identifiability conditions for skew normal mixture models, extending to multivariate distributions and deriving the characteristic function of CFUSN.

Findings

Identifiability conditions for univariate skew normal mixtures.

Extension of identifiability results to multivariate skew normal distributions.

Derivation of the characteristic function for CFUSN distribution.

Abstract

We give sufficient identifiability conditions for estimating mixing proportions in two-component mixtures of skew normal distributions with one known component. We consider the univariate case as well as two multivariate extensions: a multivariate skew normal distribution (MSN) by Azzalini and Dalla Valle (1996) and the canonical fundamental skew normal distribution (CFUSN) by Arellano-Valle and Genton (2005). The characteristic function of the CFUSN distribution is additionally derived.