Weighted Extropy for Concomitants of Upper k-Record Values Based on Huang-Kotz Morgenstern of Bivariate Distribution

In this paper, the marginal distribution of concomitants of k-record values (CKR) based on the Huang-Kotz Farlie-Gumbel-Morgenstern (HK-FGM) family of bivariate distributions is derived. In addition, we obtained the joint distribution of CKR for this family. Also, we obtained the hazard rate, reversed hazard rate, and residual life functions of CKR using the HK-FGM family. The weighted extropy and the weighted cumulative past extropy (WCPJ) are acquired for CKR under the HK-FGM family. In addition, we look into the issue of estimating the WCPJ by combining the empirical method with the concurrent use of KR in the HK-FGM family. Finally, we analyzed real-world data for illustration purposes, and the outcomes are rather striking.