Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

Mohammed Obeidat,Amer I Al-Omari,Amjad Al-Nasser

doi:10.1155/2020/7362657

Abstract

This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.

Highlights

Gompertz distribution was introduced by Gompertz [1] to describe human mortality and to establish actuarial tables
It can be seen from this plot that the differential evolution M-H (DE-M-H) chain covers a wider range of parameter values than the one obtained using RWM-H. erefore, DE-M-H is used in our simulations to obtain Bayesian estimates and credible intervals
We considered two sample sizes n 10, 20 and two values of the set size in ranked-set sample (RSS), m 2, 5. e mean and relative mean square error (MSE) of the estimators and the half length and coverage probability of the confidence intervals are provided in Tables 10 and 11

Summary

Research Article

Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling. Is paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. E proposed methods are compared via Monte Carlo simulations studies and an example employing real data. E performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples

Introduction

Update the parameter vector by

Bayes n Sampling m CP