Abstract
The main purpose of this paper is to propose an efficient non-linear estimator for estimating the population distribution function under Simple Random Sampling (SRS). The properties (Bias and Mean Square Error (MSE)) of the suggested estimator are obtained up to the first-order approximation using Taylor’s series expansion approach. The performance of the proposed estimator over some existing estimators is theoretically compared and efficiency conditions under which the proposed estimator outperforms existing estimators were obtained. The theoretical findings are supported numerically by empirical studies using five different population data sets and the result shows that the proposed estimator performed better than the existing estimators considered in the literature.