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Estimating the Components of a Mixture of Normal Distributions

N. E. Day
Biometrika
Vol. 56, No. 3 (Dec., 1969), pp. 463-474
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2334652
Stable URL: http://www.jstor.org/stable/2334652
Page Count: 12
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Estimating the Components of a Mixture of Normal Distributions
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Abstract

The problem of estimating the components of a mixture of two normal distributions, multivariate or otherwise, with common but unknown covariance matrices is examined. The maximum likelihood equations are shown to be not unduly laborious to solve and the sampling properties of the resulting estimates are investigated, mainly by simulation. Moment estimators, minimum χ2 and Bayes estimators are discussed but they appear greatly inferior to maximum likelihood except in the univariate case, the inferiority lying either in the sampling properties of the estimates or in the complexity of the computation. The wider problems obtained by allowing the components in the mixture to have different covariance matrices, or by having more than two components in the mixture, are briefly discussed, as is the relevance of this problem to cluster analysis.

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