Second-order concomitants of order statistics from bivariate Cambanis family: some information measures–estimation

Abstract

In this paper, the marginal distribution of second-order concomitants of order statistics (SCOSs) from the Cambanis family is determined. An advantageous recurrence relation between single moments of SCOSs and concomitants of order statistics (COSs) is established based on the Cambanis family. We also use this family to derive an elegant beneficial recurrence relation between single moments of the SCOSs. Some information measures, such as Shannon differential entropy, differential extropy, and negative cumulative extropy (NCEX) of SCOSs based on this family, are investigated. Furthermore, we present some numerical examples to back up the theoretical findings. In addition, a set of bivariate data from the real world was examined. Finally, an estimate of a marginal variable's scale parameter in the copula Cambanis family is obtained.