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In this paper, the Fisher information (FI), relevant to m-generalized order statistics (m-GOSs) and their concomitants of the shape-parameter of the Sarmanov family of bivariate distributions, is investigated. In addition, we study the concomitants of m-GOSs from this family. Furthermore, we look at how those concomitants were distributed collectively. The FI contained in the scale and shape parameters of the exponential and power function distributions, respectively, in concomitants of m-GOSs is obtained. A study of the asymptotic behavior of the concomitants of ordinary order statistics is also provided. Some versatile applications for this study are offered. As a final step, we examined a bivariate real-world data set for illustrative purposes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, we reveal some distributional characteristics of concomitants of generalized order statistics (GOS) with parameters that are pairwise different, arising from iterated Farlie–Gumbel–Morgenstern (IFGM) family of bivariate distributions. Additionally, the joint distribution and product moments of concomitants of GOS for this family are discussed. Moreover, some well-known information measures, i.e., extropy, cumulative residual extropy (CRJ), and negative cumulative extropy (NCJ), are derived. Applications of these results are given for order statistics, record values, and progressive type-II censored order statistics with uniform marginals distributions. Additionally, the issue of estimating the CRJ and NCJ is looked into, utilizing the empirical technique and the concomitant of GOS. Finally, bivariate real-world data sets have been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory. [ABSTRACT FROM AUTHOR]

In this paper, we study the concomitants of m-generalized order statistics (m-GOS) from the bivariate Cambanis family as an extension of several recent papers. This study can also be applied to the model of m-dual generalized order statistics (m-DGOS) as a parallel model of m-GOS. Some information measures, namely the Shannon entropy, Kullback-Leibler (KL) distance, and Fisher information number (FIN) for the concomitants of m-GOS, are derived. Furthermore, the joint distribution of concomitants of m-GOS for this family is studied. Besides, some useful recurrence relations between moments of concomitants are obtained. Moreover, the ordinary order statistics (OOS) and an important subclass of sequential order statistics (SOS) as subclasses of m-GOS, as well as the progressive type II censored order statistics (POS) as a more general subclass of GOS, are separately discussed. Finally, an application of these results is given for bivariate generalized exponential distribution. [ABSTRACT FROM AUTHOR]

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ 1 , ... , γ n 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. [ABSTRACT FROM AUTHOR]