Document Type : Original Article

Authors

• Haroon Barakat ¹
• Islam Husseiny ²

¹ Professor of Mathematical Statistics-Faculty of Science-Zagazig University-Egypt

² Lecturer of Statistics-Faculty of Science-Zagazig University-Zagazig-Egypt

Abstract

Let $\{(X_i,Y_i), i\geq1\}$ be a sequence of bivariate random variables (RVs)

from a continuous distribution. If $\{R_{n}, n\geq1\}$ is the sequence of record

values in the sequence $\{X_i\},$ then the RV $Y_i,$ which corresponds to $R_n$ is called the concomitant of the $n$th-record, denoted by $R_{[n]}.$ In this paper, we study the Shannon's entropy of $R_{[n]}$ and $(R_{n},R_{[n]}),$ under iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate distribution. In addition, we find the Kullback-Leibler distance (K-L distance) between $R_{[n]}$ and $R_{n}.$ Moreover, we study the Fisher information matrix (FIM) for record values and their concomitants about the shape-parameter vector of IFGM bivariate distribution. Also, we study the relative efficiency-matrix of that vector-estimator of the shape-parameter vector whose covariance matrix is equal to Cram\'{e}r-Rao lower bound, based on record values and their concomitants and i.i.d observations. 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.

Keywords

• Iterated FGM copula
• Concomitants
• Shannon'
• s entropy
• Fisher information
• Kullback-Leibler distance
• Fisher information number

Main Subjects

• Information Theory