The Annals of Mathematical Statistics

Identifiability of Finite Mixtures

Henry Teicher

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Abstract

In general, the class of mixtures of the family of normal distributions or of Gamma (Type III) distributions or binomial distributions is not identifiable (see [3], [4] or Section 2 below for the meaning of this statement). In [4] it was shown that the class of all mixtures of a one-parameter additively-closed family of distributions is identifiable. Here, attention will be confined to finite mixtures and a theorem will be proved yielding the identifiability of all finite mixtures of Gamma (or of normal) distributions. Thus, estimation of the mixing distribution on the basis of observations from the mixture is feasible in these cases. Some separate results on identifiability of finite mixtures of binomial distributions also appear.

Article information

Source
Ann. Math. Statist. Volume 34, Number 4 (1963), 1265-1269.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177703862

Digital Object Identifier
doi:10.1214/aoms/1177703862

Mathematical Reviews number (MathSciNet)
MR155376

Zentralblatt MATH identifier
0137.12704

JSTOR
links.jstor.org

Citation

Teicher, Henry. Identifiability of Finite Mixtures. Ann. Math. Statist. 34 (1963), no. 4, 1265--1269. doi:10.1214/aoms/1177703862. https://projecteuclid.org/euclid.aoms/1177703862


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