Pitman's Measure of Closeness for Weighted Random Variables

* Statistical inference based on weighted random variables is developed in the sense of Pitman's measure of closeness. Some general formulas are presented to compute the Pitman closeness of two weighted random variables to the parameter of interest. A new general weighted model is also introduced and some properties are investigated. Also, the concept of Pitman's measure of closeness is used for measuring the nearness of some weighted random variables with respect to each other. The results are illustrated using some real data sets. Eventually, some conclusions are stated. Keywords: * weighted distribution; exponential distribution; ordered data; population quantile; skew distributions.