ESTIMATION OF THE LARGEST LOCATION PARAMETER OF EXPONENTIAL-DISTRIBUTIONS

Independent random samples (of possibly unequal sample sizes) are drawn from k (greater-than-or-equal-to 2) exponential populations having unknown location parameters lambda1,...,lambda(k) and known scale parameters sigma1,...,sigma(k). The problem of estimating theta(k)=max(lambda1,...,lambda(k)) is investigated. Under the squared error loss function, some estimators which are better than the usual estimators are obtained. These estimators are also compared with respect to the Pitman's (1937) measure of closeness.