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.
Keywords
MathematicsEstimatorUnivariateCovarianceStatisticsMultivariate normal distributionApplied mathematicsCovariance matrixSampling (signal processing)Mixture modelComputationMultivariate statisticsMoment (physics)Restricted maximum likelihoodMaximum likelihoodAlgorithmComputer science
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Publication Info
- Year
- 1969
- Type
- article
- Volume
- 56
- Issue
- 3
- Pages
- 463-474
- Citations
- 821
- Access
- Closed
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Cite This
N. E. Day
(1969).
Estimating the components of a mixture of normal distributions.
Biometrika
, 56
(3)
, 463-474.
https://doi.org/10.1093/biomet/56.3.463
Identifiers
- DOI
- 10.1093/biomet/56.3.463