Estimation of Common Scale Parameter of Several Heterogeneous Pareto Populations Based on Records

Abstract

This article deals with the problem of estimation of common scale parameter $$\theta$$ of k Pareto populations with unknown and unequal shape parameters $$\alpha _1,\alpha _2,\ldots,\alpha _k$$ based on record data. We derive the maximum likelihood estimator (MLE), the modified MLE and the uniformly minimum variance unbiased estimator (UMVUE) of $$\theta$$ . Under the scaled squared error loss function, a class of improved estimators over the MLE of $$\theta$$ is derived. This class of improved estimators contains the modified MLE as well as the UMVUE of $$\theta$$ . A simulation study is carried out for comparing the performances of the estimators of $$\theta$$ . Further, a real data example is provided to illustrate the computation of various estimators of $$\theta$$ .