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

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 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.

Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings

“…The literature teems with several results of the Shannon entropy and its related measures. Interested readers may refer to [14][15][16][17][18] for the Shannon entropy, Kullback-Leibler divergence, and Fisher information number; [19,20] for fractional cumulative residual entropy and cumulative residual entropy, respectively; [13,[21][22][23][24] for the Tsallis entropy and its related measures; and finally [25,26] for the extropy and Rényi entropy and its applications, respectively.…”

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Sarmanov bivariate distribution: dependence structure—Fisher information in order statistics and their concomitants

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