Different estimation methods and joint con dence regions for the parameters of a generalized inverted family of distributions

Abstract

In this paper, we deal with the problem of estimating the parameters ofa generalized inverted family of distributions. We propose the inversemoment and modifed inverse moment estimators of the parameters.The existence and uniqueness of inverse moment and modifed inversemoment estimators is derived. Monte Carlo simulations are conductedto compare their performances with maximum-likelihood estimators.Two methods for constructing joint confdence regions for the two parametersare also proposed and their performances are discussed. Anumerical example is presented to illustrate the methods.