Fisher Information and Shannon’s Entropy for Record Values and Their Concomitants under Iterated FGM Family

• Published in: Romanian journal of physics 2024-01, Vol.69 (1-2), p.103-103
• Main Authors: ABD ELGAWAD, M. A., BARAKAT, H. M., ABDELWAHAB, M. M., ZAKY, M. A., HUSSEINY, I. A.
• Format: Article
• Language: English
• ISSN: 1221-146X
• DOI: 10.59277/RomJPhys.2024.69.103

Let {(Xi ,Yi), i ≥ 1} be independent and identically distributed random variables (RVs) from a continuous bivariate distribution. If {Rn,n ≥ 1} is the sequence of upper record values in the sequence {Xi}, then the RV Yi, which corresponds to Rn is called the concomitant of the nth record, denoted by R[n]. We study the Shannon entropy (SHANE) of R[n] and (Rn,R[n]) under iterated Farlie-Gumbel-Morgenstern (IFGM) family. In addition, we find the Kullback-Leibler distance (K-L) between R[n] and Rn. Moreover, we study the Fisher information matrix (FIM) for record values and their concomitants about the shape-parameter vector of the IFGM family. Also, we study the relative efficiency matrix of that vector-estimator of the shape-parameter vector whose covariance matrix is equal to Cramer-Rao lower bound, based on record ´ values and their concomitants. In addition, the Fisher information number (FIN) of R[n] is derived. Finally, we evaluate the FI about the mean of exponential distribution in the concomitants of record values.