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Biometrika 1970 57(1):215-217; doi:10.1093/biomet/57.1.215
© 1970 by Biometrika Trust
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MISCELLANEA

On a mixture of normal distributions

JAVAD BEHBOODIAN

Pahlavi University Shiraz, Iran

In a mixture of k normal distributions the maximum likelihood estimates of µj and {sigma}2j, forj = 1, ..., k, can be expressed by a weighted sample mean and a weighted sample variance, and the maximum likelihood estimates of the over-all mean and variance of the mixture coincide with the sample mean and sample variance.


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