Estimation of the population distribution function is an important problem in survey sampling with a variety of applications in social sciences, medical studies, environmental research and economics and in industrial quality control. When auxiliary information is not effectively used, the existing estimators under simple random sampling (SRS) may have low precision. This study considers a novel enhanced estimator for the population distribution function based on the use of two auxiliary variables which are correlated with the study variable, motivated by the desire to improve estimation accuracy and stability. The proposed estimator is based on simple random sampling and the bias and mean square error expressions are derived to first order of approximation. Mean square error and percentage relative efficiency are used to assess the efficiency of the estimator. An empirical validation is performed through a numerical investigation using simulated and real data sets. It is found that the proposed estimator is more efficient and stable, and more accurate than traditional estimators under realistic sampling condition. So, the proposed methodology is reliable and practically useful for contributing to the development of efficient estimation procedures in sampling theory and applications.
Ahmad et al. (Wed,) studied this question.
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