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In this study, we obtain the maximum likelihood (ML) and the modified maximum likelihood (MML) estimators for the location and the scale parameters of the Jones and Faddy’s Skew t (JFST) distribution based on the doubly Type II censored samples. Then, we use the Monte Carlo (MC) simulation study to compare the efficiencies of the ML and the MML estimators. The MC simulation study shows that, MML estimators have more or less same efficiency with the corresponding ML estimators. At the end of the study, it can be concluded that if we focus on the efficiencies of the estimators, we prefer to use ML estimators. However, if we focus on the computational difficulties together with the efficiencies of the estimators, we prefer to use MML estimators. [ABSTRACT FROM AUTHOR]