Weighted Analogue of Inverse Gamma Distribution: Statistical Properties, Estimation and Simulation Study

Abstract

In this article we propose a new weighted version of inverse Gamma distribution known as Weighted Inverse Gamma distribution (WIGD). We examine the Length biased and Area biased versions of Weighted Inverse Gamma distribution. Basic structural properties viz moments, mode, moment generating function (mgf), characteristic function (cf), hazard rate function and measures of uncertainty. The parameters of this model are estimated from both classical (namely, maximum likelihood estimator and method of moments, and compare them by using extensive numerical simulations) and Bayesian point of view. The Bayes estimates are estimated by using non-informative Jeffrey’s prior and informative Inverse Chi square prior under different types of loss function (symmetric and asymmetric loss functions). Finally, a simulation study has been conducted for comparing weighted inverse gamma distribution with other competing distributions.