MLE in Two Normal Samples with Equal but Unknown Population Coefficients of Variation

Abstract

Maximum likelihood estimates are derived for the parameters of two normal populations with coefficients of variation equal but unknown. Formulas are provided for calculating the asymptotic variances and covariances of the estimates. The relative efficiency of the proposed mean estimator with respect to the sample mean is shown to be greater than one. The effect of departures from the assumptions of normality and of equal coefficients of variation on this relative efficiency are studied. An example is provided with data from wildlife populations to illustrate the proposed methods.

Key Words:

• Maximum likelihood
• Coefficient of variation
• Two-sample problem