Research Article Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling Mohammed Obeidat , 1,2 Amjad Al-Nasser, 2 and Amer I. Al-Omari 3 1 Department of Quantitative Methods, King Faisal University, Hofuf, Saudi Arabia 2 Department of Statistics, Yarmouk University, Irbid, Jordan 3 College of Business Administration, Al Falah University, Dubai, UAE Correspondence should be addressed to Mohammed Obeidat; mobeidat@kfu.edu.sa Received 2 April 2020; Revised 12 July 2020; Accepted 29 July 2020; Published 7 September 2020 Academic Editor: Ram´ on M. Rodr´ ıguez-Dagnino Copyright © 2020 Mohammed Obeidat et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is 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 pa- rameters 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. 1.Introduction Gompertz distribution was introduced by Gompertz [1] to describe human mortality and to establish actuarial tables. It was also found to be useful in medical sciences because it gives a good fit to data coming from clinical trials on ordered subjects [2]. Gompertz distribution has been extensively studied in the literature (see, for example, El-Din et al. [3] and the reference therein). is paper focuses on the three- parameter generalized Gompertz distribution, which was proposed by El-Gohary et al. [4]. A random variable X is said to have a generalized Gompertz (GG) distribution with parameter vector θ �(λ, c, θ), denoted as X: GG(λ, c, θ), if its probability density function and its distribution function are given by f(x; λ, c, θ)� θλe cx e − λ/ce cx − 1 ( ) 1 − e − λ/ce cx − 1 ( )   θ− 1 , x > 0, λ, θ > 0,c ≥ 0, (1) F(x; λ, c, θ)� 1 − e − λ/ce cx − 1 ( )   θ , x > 0, λ, θ > 0,c ≥ 0. (2) e GG distribution covers the generalized exponential distribution and the one-parameter exponential distribu- tion as special cases when c goes to zero and θ � 1. It also covers the Gompertz distribution when θ � 1. e GG distribution takes different shapes of the failure rate curve, namely, increasing, constant, decreasing, or bathtub depending on the value of θ (the shape parameter). e GG distribution is considered as a strong candidate Hindawi Journal of Probability and Statistics Volume 2020, Article ID 7362657, 14 pages https://doi.org/10.1155/2020/7362657