The Annals of Statistics

On Estimating the Common Mean of Two Normal Distributions

Arthur Cohen and Harold B. Sackrowitz

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Consider the problem of estimating the common mean of two normal distributions. Two new unbiased estimators of the common mean are offered for the equal sample size case. Both are better than the sample mean based on one population for sample sizes of 5 or more. A slight modification of one of the estimators is better than either sample mean simultaneously for sample sizes of 10 or more. This same estimator has desirable large sample properties and an explicit simple upper bound is given for its variance. A final result is concerned with confidence estimation. Suppose the variance of the first population, say, is known. Then if the sample mean of that population, plus and minus a constant, is used as a confidence interval, it is shown that an improved confidence interval can be found provided the sample sizes are at least 3.

Article information

Ann. Statist., Volume 2, Number 6 (1974), 1274-1282.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F10: Point estimation
Secondary: 62C15: Admissibility

Common mean unbiased estimators minimax estimators confidence intervals inter-block information


Cohen, Arthur; Sackrowitz, Harold B. On Estimating the Common Mean of Two Normal Distributions. Ann. Statist. 2 (1974), no. 6, 1274--1282. doi:10.1214/aos/1176342878.

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  • See Correction: Arthur Cohen, Harold B. Sackrowitz. Notes: Correction to "On Estimating the Common Mean of Two Normal Distributions". Ann. Statist., vol. 4, no. 6 (1976), 1294.