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

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.