Notes on Entropy for Concomitants of Record Values in Farlie-Gumbel-Morgenstern (FGM) Family

Abstract

Let {(Xi; Yi), i ≥ 1} be a sequence of bivariate random variables from a continuous distribution. If {R(subscript n), 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(subscript [n]). In FGM family, we determine the amount of information contained in R(subscript [n]) and compare it with amount of information given in R(subscript n). 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 R(subscript n) and R(subscript [n]) in the copula model of FGM family.