A new condition for identifiability of finite mixture distributions

Abstract

In this paper a sufficient condition for the identifiability of finite mixtures is given. This condition is less restrictive than Teicher’s condition (Teicher H, Ann Math Stat 34:1265–1269 (1963)) and therefore it can be applied to a wider range of families of mixtures. In particular, it applies to the classes of all finite mixtures of Log-gamma and of reversed Log-gamma distributions. These fami-lies have been already studied by Henna J Jpn Stat Soc 24:193–200 (1994) using another condition, different from Teicher’s, but more difficult to check in many cases. Furthermore, the result given in this paper is very appropiated for the case of mixtures of the union of different distribution families. To illustrate this an applica-tion to the class of all finite mixtures generated by the union of Lognormal, Gamma and Weibull distributions is given, where Teicher’s and Henna’s conditions are not applicable.