Robust ratio estimators of population mean for skewed and contaminated population

The efficiency of the traditional ratio estimator decreases with the presence of outliers, inliers or when the underlying distribution is not normal. To improve the efficiency, we propose new robust ratio estimators utilizing the Lloyd's robust estimator and modified maximum likelihood estimator (MMLE), and provide their theoretical properties. We calculate the mean square error and relative efficiency of the proposed estimators and compare its performance with some other existing traditional estimators via a simulation study under various contamination or misspecification models. Further, we evaluate the exact value of the mean square error and to compare the performance of the proposed estimators using the numerical illustrations.