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Keywords = Huang–Kotz FGM family

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18 pages, 399 KiB  
Article
Scrutiny of a More Flexible Counterpart of Huang–Kotz FGM’s Distributions in the Perspective of Some Information Measures
by Mohamed A. Abd Elgawad, Haroon M. Barakat, Doaa A. Abd El-Rahman and Salem A. Alyami
Symmetry 2023, 15(6), 1257; https://doi.org/10.3390/sym15061257 - 14 Jun 2023
Cited by 2 | Viewed by 1667
Abstract
In this work, we reveal some distributional traits of concomitants of order statistics (COSs) arising from the extended Farlie–Gumbel–Morgenstern (FGM) bivariate distribution, which was developed and studied in recent work. The joint distribution and product moments of COSs for this family are discussed. [...] Read more.
In this work, we reveal some distributional traits of concomitants of order statistics (COSs) arising from the extended Farlie–Gumbel–Morgenstern (FGM) bivariate distribution, which was developed and studied in recent work. The joint distribution and product moments of COSs for this family are discussed. Moreover, some useful recurrence relations between single and product moments of concomitants are obtained. In addition, the asymptotic behavior of the concomitant’s rank for order statistics (OSs) is studied. The information measures, differential entropy, Kullback–Leibler (KL) distance, Fisher information number (FIN), and cumulative past inaccuracy (CPI) are theoretically and numerically studied. Full article
(This article belongs to the Section Mathematics)
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17 pages, 340 KiB  
Article
Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution
by Mohamed A. Abd Elgawad, Haroon M. Barakat, Shengwu Xiong and Salem A. Alyami
Entropy 2021, 23(3), 335; https://doi.org/10.3390/e23030335 - 12 Mar 2021
Cited by 17 | Viewed by 2210
Abstract
In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between [...] Read more.
In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics. Full article
(This article belongs to the Special Issue Entropies, Divergences, Information, Identities and Inequalities)
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