Measures of information for concomitants of generalized order statistics from subfamilies of Farlie–Gumbel–Morgenstern distributions

Abstract

In this paper, we study Shannon's entropy and Fisher information number for concomitants of generalized order statistics from subfamilies of Farlie-Gumbel-Morgenstern when the marginal distributions are Weibull, exponential, Pareto and power function. Also, we provide some numerical results of Shannon entropy and Fisher information number for concomitants of order statistics.Mathematics Subject Classification 62B10 · 62H99 · 62P99

Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution

“…It is worth mentioning that some results in [38] are doubtful. For example, the FI number defined by (15) seems to be wrong, because we have −1 ≤ αC (r, n, m, k) ≤ 1, which implies that log(−1 + αC (r, n, m, k)) and log(−1 − αC (r, n, m, k)) have no meaning, since −2 ≤ −1 + αC (r, n, m, k) ≤ 0 and −2 ≤ −1 − αC (r, n, m, k) ≤ 0.…”

“…Moreover, Mohie El-Din et al [38] studied the Shannon entropy and the FI number for the concomitants of m-GOSs from FGM family for some special known marginals. Recently, Abd Elgawad et al [10] studied the FI number for concomitants of m-DGOSs in the HK-FGM family.…”

“…Recently, Abd Elgawad et al [10] studied the FI number for concomitants of m-DGOSs in the HK-FGM family. As a natural extension of the results obtained by [30,38], we study the concomitants of DGOSs (in the case when γ i = γ j , i = j, i, j = 1, 2, . .…”

On concomitants of ordered random variables under general forms of Morgenstern family

“…Theorem 2.4. Based on Bairamov extension with pd f given by (5) and cd f given by (4) (with p 1 = p 2 = 1), utilizing (7), (15) and (13), the pd f and cd f of the concomitant of rth case-II of os, Y [r;n, m,k] , are given by, 1 ≤ r ≤ n, respectively:…”