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Notes on Entropy for Concomitants of Record Values in Farlie-Gumbel-Morgenstern (FGM) Family
Volume 11, Issue 1 (2013), pp. 59–68
Saeid Tahmasebi  

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https://doi.org/10.6339/JDS.2013.11(1).1104
Pub. online: 4 August 2022      Type: Research Article      Open accessOpen Access

Published
4 August 2022

Abstract

Abstract: Let {(Xi , Yi), i ≥ 1} be a sequence of bivariate random variables from a continuous distribution. If {Rn, n ≥ 1} is the sequence of record values in the sequence of X’s, then the Y which corresponds with the nth record will be called the concomitant of the nth-record, denoted by R[n] . In FGM family, we determine the amount of information contained in R[n] and compare it with amount of information given in Rn. Also, we show that the Kullback-Leibler distance among the concomitants of record values is distribution-free. Finally, we provide some numerical results of mutual information and Pearson correlation coefficient for measuring the amount of dependency between Rn and R[n] in the copula model of FGM family.

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Keywords
Concomitants Farlie-Gumbel-Morgenstern family mutual information

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