ON RELIABILITY ESTIMATION IN THE WEIBULL CASE

Abstract

The asymptotic mean integrated squared errors of the naive estimator, the maximum likelihood estimator, the uniformly minimum variance unbiased estimator, and the invariantly optimal estimator of a reliability function are calculated in the Weibull distribution case. These estimators are also compared using the concept of the asymptotic deficiency. Further, it is shown that, after bias-adjustment, the later three estimators have the same asymptotic mean integrated squared error up to the order o(n^-2), where n is a size of sample.