A New Estimation Method Based on Order Statistics in the Families of Symmetric Location-scale Distributions

In this study, new unbiased and nonlinear estimators based on order statistics are proposed for the family of symmetric location-scale distributions and these estimators can be computed from both uncensored and symmetric doubly Type II censored samples. In addition, other relevant unbiased estimators are proposed to estimate standard deviations of these new estimators. A simulation study has been performed to evaluate the performance of the new estimators compared to BLU estimators for small sample sizes. As a result of the simulation study, the new estimators proposed for the location-scale family in general performed nearly as good as BLU estimators. Furthermore, the computational advantage of the proposed estimators over BLU and ML estimators are worthy of notice. In addition, these new estimators have been applied to real data, and the estimation results obtained have been compatible with those of BLUE methods.