On A Shape Parameter of Gompertz Inverse Exponential Distribution Using Classical and Non Classical Methods of Estimation

Abstract

The Gompertz inverse exponential distribution is a three-parameter lifetime model with greater flexibility and performance for analyzing real life data. It has one scale parameter and two shape parameters responsible for the flexibility of the distribution. Despite the importance and necessity of parameter estimation in model fitting and application, it has not been established that a particular estimation method is better for any of these three parameters of the Gompertz inverse exponential distribution. This article focuses on the development of Bayesian estimators for a shape of the Gompertz inverse exponential distribution using two non-informative prior distributions (Jeffery and Uniform) and one informative prior distribution (Gamma prior) under Square error loss function (SELF), Quadratic loss function (QLF) and Precautionary loss function (PLF). These results are compared with the maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under Quadratic loss function (QLF) with any of the three prior distributions provide the smallest mean square error for all sample sizes and different values of parameters.

Estimation of a Shape Parameter of a Gompertz-lindley Distribution Using Bayesian and Maximum Likelihood Methods

“…This paper has made use of two non-informative priors (uniform and Jeffrey) and an informative prior (gamma) to estimate the shape parameter of a GomLinD. These assumed priors distributions or beliefs have been used over the years by several authors including [34][35][36][37][38][39][40][41][42]. Our article also considered three loss functions which are squared error, quadratic and precautionary loss functions and these loss functions have been studied by other authors [43][44][45][46][47][48][49][50][51] etc.…”

Estimating the Shape Parameter of the Exponential-Weibull Distribution using Bayesian Technique

“…Bayesian technique has received increasing attention by researchers. For example, Eraikhuemenet al (2020a), Ieren et al (2020), Eraikhuemen et al (2020b), Ieren and Oguntunde (2018), Preda et al (2010), Dey (2010), Aliyu andYahaya (2016), Ahmad et. al.…”