Cramér-Rao Efficiencies of Best Linear Invariant Estimators of Parameters of the Extreme-Value Distribution Under Type II Censoring from Above

Abstract

If, in life testing, failure time has the two-parameter Weibull distribution, then the random variable log failure time has the first asymptotic distribution of smallest (extreme) values. Let loss be squared error divided by the square of a scale parameter of this distribution, and consider linear estimators, with expected loss invariant under location and scalar transformations, of parametric functions of a distribution location parameter u and scale parameter b. It has been shown that the best among these linear invariant estimators can be calculated as a function of the best linear unbiased (BLU) estimators of u and b and their covariance matrix. Moreover, the expected loss of any best linear invariant (BLI) estimator is uniformly less than that of the corresponding BLU estimator. In the present paper expressions are derived for Cramer-Rao bounds for the mean squared error of regular invariant estimators, of parametric functions of general location and scale parameters, based on the first r ordered obs...