Pitman closeness of current k-records to population quantiles

In this paper, the Pitman’s measure of closeness of current k-records to the population quantiles is investigated. While the required probabilities typically depend on the underlying distribution, in this article, we show that they are distribution-free for the symmetric distributions. The exact expressions are derived for the case of uniform and exponential distributions. A real data set will be used to illustrate the results of the paper. Eventually, some conclusions are presented.