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Mathematics 2019, 7(2), 175; https://doi.org/10.3390/math7020175

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

1
Department of Statistics, Persian Gulf University, Bushehr 7516913817, Iran
2
Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy
*
Author to whom correspondence should be addressed.
Received: 17 December 2018 / Revised: 31 January 2019 / Accepted: 5 February 2019 / Published: 14 February 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
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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. View Full-Text
Keywords: measure of information; cumulative inaccuracy; mutual information; lower record values measure of information; cumulative inaccuracy; mutual information; lower record values
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Eskandarzadeh, M.; Di Crescenzo, A.; Tahmasebi, S. Cumulative Measure of Inaccuracy and Mutual Information in k-th Lower Record Values. Mathematics 2019, 7, 175.

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