Parameter estimation of the power lindley distribution with the optimal b-robust estimation method

In this thesis, parameter estimates of the power Lindley (PL) distribution were obtained by using the maximum likelihood (ML) and least squares (LS) estimation methods, which are among the known classical methods. Besides, it is known that classical estimation methods are very sensitive to outliers when there are outliers in the data. Therefore, an alternative estimation method against classical estimation methods is needed that will not be affected by outliers. In this thesis, robust estimators for the parameters of the PL distribution were obtained using the optimal B-robust (OBR) estimation method. To compare the performances of the proposed estimators and to provide variety in the simulation study, the estimators for the parameters of the PL distribution were also obtained using the robust regression (RR) estimation method. A real data application was also performed to test the applicability of the OBR estimators. In the simulation study, in the presence and absence of the outliers, the performances of OBR estimators were compared with the performances of the estimators (ML, LS, RR). At the same time, the performances of the estimators were also compared on the actual real data including outliers. As a result of the simulation study and real data application, it was observed that the OBR estimators showed the best performance when there were outliers in the data. Consequently, it is appropriate to use the OBR estimation method for the parameters of the PL distribution when there are outliers in the data.