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

Abstract

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