A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions

A simple proof of the identification of a mixture of two univariate normal distributions is given. The proof is based on the equivalence of local identification with positive definiteness of the information matrix and the equivalence of the latter to a condition on the score vector that is easily checked for this model. Two extensions using the same line of proof are also given. We would like to thank Tom Wansbeek, Michel Wedel, Arie Kapteyn, and two anonymous reviewers for helpful comments on earlier versions of this paper.