Identifiability of Finite Mixtures - with Applications to Circular Distributions

Abstract

A general result about identifiability and strong identifiability of finite mixtures of a family of distributions is obtained via tail conditions on the corresponding characteristic functions. This is applied to location-scale families on the real line and to circular distributions. Particular cases include circular wrapped distributions of location-scale families, stable distributions and the d-dimensional wrapped normal distribution. Finally, counter examples are given which highlight differences between identifiability on the real line and on the circle.