Abstract
In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters 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.
Highlights
In testing the strength of materials, reliability analysis, lifetime studies, etc. the realizations of experiments arise in nondecreasing order and, we need to consider several models of ascendingly ordered random variables (RVs)
Many of such models, such as ordinary order statistics, order statistics with non-integral sample size, sequential order statistics, record values, Pfeifer’s record model and progressive type-II censored order statistics (POSs), are contained in what is known as the generalized order statistics (GOSs)
As a natural extension of the results obtained by [30,38], we study the concomitants of dual GOSs (DGOSs) from the HK–FGM model
Summary
In testing the strength of materials, reliability analysis, lifetime studies, etc. the realizations of experiments arise in nondecreasing order and, we need to consider several models of ascendingly ordered random variables (RVs). The distributional properties and some important information measures such as FI number and Shannon’s entropy of the concomitants of GOSs and DGOSs from some important extensions of the FGM model, such as the HK–FGM model, were recently studied in [10,11,12,13,14,15]. All of these studies were carried out for the submodels m-GOSs and m-DGOSs, which include many interesting models such as ordinary order statistics and sequential order statistics.
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