Robust estimation of the location and the scale parameters of shifted Gompertz distribution

Abstract

In this study, we consider the estimation of the location parameter  and the scale parameter  of the shifted Gompertz (SG) distribution. We obtain the closed form estimators of these parameters by using the modified maximum likelihood (MML) methodology originated by Tiku (1967). We also compare the efficiencies of these estimators with the well-known and widely used least squares (LS) and maximum likelihood (ML) estimators via Monte-Carlo simulation study in terms of bias, mean square error (MSE) and deficiency (Def) criteria. In addition, we evaluate the performances of the proposed estimators when the data contains the outliers or is contaminated. In other words, the robustness properties of the estimators are investigated. A real data set is analyzed to demonstrate the implementation of the estimation methods at the end of the study.