Cumulative Measure of Inaccuracy and Mutual Information in k-th Lower Record Values

Abstract

In this paper, we discuss the cumulative measure of inaccuracy in k-lower record values and study characterization results of dynamic cumulative inaccuracy. We also present some properties of the proposed measures, and the empirical cumulative measure of inaccuracy in k-lower record values. We prove a central limit theorem for the empirical cumulative measure of inaccuracy under exponentially distributed populations. Finally, we analyze the mutual information for measuring the degree of dependency between lower record values, and we show that it is distribution-free.