Comparisons among some predictors of exponential distributions using Pitman closeness

The bias, mean squared error and likelihood optimality criteria are used frequently to compare estimators and predictors. Recently, the probability of nearness around a statistic (estimator or predictor) has received a considerable attention in the literature. In this article, we adopt the Pitman’s measure of closeness (PMC) as an optimality criterion to compare the maximum likelihood, best linear unbiased, best linear invariant, median unbiased and conditional median predictors of a future ordered statistic based on a type II censored sample from an exponential distribution with unknown scale parameter. Numerical computations of the PMC for all comparisons among these predictors are performed and presented.