The Ranked Sample-Mean Monte Carlo Method for Unidimensional Integral Estimation

This study introduced the idea of using the novel ranked set sampling scheme for the Monte Carlo integral estimation problem. We proposed and discussed the unidimensional integral problem. It is demonstrated that this approach provides an unbiased and more efficient estimators than the traditional estimators based on simple random sampling. The method is illustrated by examples for estimating π and {f (x) = e-x2, 0≤x≤1}. An application to estimate the Gini index is proposed.