ESTIMATION OF ORDERED LOCATION PARAMETERS - THE EXPONENTIAL-DISTRIBUTION

The problem of component wise estimation of ordered location parameter s theta1 and theta2 (theta1 less-than-or-equal-to theta2) of two indep endent exponential distributions is investigated. The scale parameters are assumed to be unequal but known. Independent random samples of un equal sample sizes are drawn from two populations and the estimators a dmissible among the mixed estimators of theta1 and theta2 are obtained . It is shown that the minimum risk estimators (MREs) of theta1 and th eta2 without assuming theta1 less-than-or-equal-to theta2 are inadmiss ible when one does assume that theta1 less-than-or-equal-to theta2. Th e efficiencies of mixed estimators relative to MREs (without assuming theta1 less-than-or-equal-to theta2) are tabulated for equal sample si zes and equal scale parameters. AMS 1980 subject classification: Prima ry 62G05; secondary 62N05.