Robust ratio and product based estimators using known auxiliary information through modified maximum likelihood

In this paper, we consider the situation where the underlying distribution of the study variable is not normally distributed. Under such situations, we propose ratio and product based estimators for the finite population mean in simple random sampling using known auxiliary information based on order statistics. We obtain the expressions for biases and mean square errors (MSEs) of the proposed estimators, which show that the proposed estimators have less MSEs and biases than other existing estimators. Simulations have been studied under various super-population models. A real life application is also provided. Robustness properties of the proposed estimators have been studied via simulations. Confidence intervals (CIs) show that the proposed estimators have shorter CIs of estimates than those of the existing estimators.