Open Access
Translator Disclaimer
November, 1974 On Estimating the Common Mean of Two Normal Distributions
Arthur Cohen, Harold B. Sackrowitz
Ann. Statist. 2(6): 1274-1282 (November, 1974). DOI: 10.1214/aos/1176342878


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.


Download Citation

Arthur Cohen. Harold B. Sackrowitz. "On Estimating the Common Mean of Two Normal Distributions." Ann. Statist. 2 (6) 1274 - 1282, November, 1974.


Published: November, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0294.62037
MathSciNet: MR365851
Digital Object Identifier: 10.1214/aos/1176342878

Primary: 62F10
Secondary: 62C15

Keywords: Common mean , confidence intervals , inter-block information , minimax estimators , unbiased estimators

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 6 • November, 1974
Back to Top