In this paper, we study the concomitants of generalized order statistics from iterated Farlie-Gumbel-Morgenstern (FGM) bivariate distribution. Three information measures, the Shannon entrop...

In this paper, we study the extropy for concomitants of m−generalized order statistics (m−GOSs) from Huang–Kotz–Farlie–Gumbel–Morgenstern (HK‐FGM) bivariate distribution. Moreover, the cumulative residual extropy (CREX) and negative cumulative extropy (NCEX) are depicted. Furthermore, the empirical technique in conjunction with the concomitant of m−GOS is used to investigate the problem of estimating the CREX and NCEX. The concomitants of order statistics and record values are offered as some applications of these findings.

One of the most efficient and robust methods in estimation is to find the Fisher information matrix (FIM). In this paper, the FIM concerning order statistics (OSs) and their concomitants about the shape-parameter vector of Cambanis bivariate distribution is derived. This method contains information conveyed by singly or multiply censored bivariate samples drawn from the Cambanis bivariate distribution. In addition, we obtain and study the Fisher information (FI) about the mean and shape parameters in the concomitants of OSs for this bivariate distribution based on exponential and power function distributions. Finally, the information entropy of Shannon in the OSs and their concomitants based on the Cambanis distribution is studied. Some numerical computations were performed on the FI which lend support to the theoretical results.

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.

We propose a more flexible symmetric counterpart of the Huang–Kotz’s copula of the 1st type. Both the counterpart and Huang–Kotz’s copula of the 1st type provide the same improvement in the correlation level. Moreover, the proposed copula includes special cases of many other extensions of the Farlie–Gumbel–Morgenstern (FGM) copula.