On the Identifiability of Finite Mixtures Based on the Union of Logarithmic Series and Discrete Rectangular Families

Abstract

In this paper, finite mixtures of the union of Logarithmic Series and Discrete Rectangular families are proved to be identifiable. The sufficient condition for the identifiability of finite mixtures given by Atienza et al. (Metrika 63:215-221, 2006) is applied instead of mostly used Teicher's condition (Teicher, Ann Math Stat 34: 1265-1269, 1963). The choice of distribution is made in order to stress the fact that, contrarily to Teicher's approach, Atienza et al.'s theorem being used does apply to heterogeneous parametric families.