What is Empirical Distribution Function

Order statistics refer to the collection of sample observations sorted in ascending order and are among the most fundamental tools in non-parametric statistics and inference. Statistical inference established based on order statistics assumes nothing stronger than continuity of the cumulative distribution function of the population and is simple and broadly applicable. We discuss how order statistics are applied in computer simulation, e.g., tests of independence, tests of goodness of fit, hypothesis tests of equivalence of means, ranking and selection, and quantiles estimation. These order-statistics techniques are key components of many simulation studies.