Estimation of common scale parameter of several heterogeneous exponential populations based on generalized order statistics

In this article, classical and Bayesian estimation procedures are followed to estimate the common scale parameter σ of several shifted exponential populations with different unknown location parameters μi, i = 1,…, k, based on generalized order statistics. The estimators are obtained for both restricted and unrestricted parameter spaces of μi. In the classical approach, we obtained the MLE, UMVUE and MREE for σ. Then, a Bayesian study is conducted to estimate σ under the scaled-squared error loss function using some suitable priors. Further, a general result is derived for inadmissibility of MREE under the scaled-squared error loss function. A simulation study is conducted for comparing the estimators for two special cases of generalized order statistics, namely, progressive type II censored order statistics and record values. Further, two real data sets are used to show the performance of the proposed estimators.