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

[摘要] 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.

[学科分类] 土木及结构工程学

[关键词] Concomitants;Farlie-Gumbel-Morgenstern family;mutual information