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

Maryam Eskandarzadeh, Antonio Di Crescenzo and Saeid Tahmasebi
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Maryam Eskandarzadeh: Department of Statistics, Persian Gulf University, Bushehr 7516913817, Iran
Antonio Di Crescenzo: Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy
Saeid Tahmasebi: Department of Statistics, Persian Gulf University, Bushehr 7516913817, Iran

Mathematics, 2019, vol. 7, issue 2, 1-19

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.

Keywords: measure of information; cumulative inaccuracy; mutual information; lower record values (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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