Sarmanov Family of Bivariate Distributions: Statistical Properties—Concomitants of Order Statistics—Information Measures

Sarmanov family of bivariate distributions, which was suggested by Sarmanov (Mathematical models in hydrology symposium, 1974) as a new mathematical model of hydrological processes, is considered one of the most flexible and efficient extended families of the traditional FGM family. Despite its manifest advantages, it was never investigated in the literature. In this paper, we revisit this family by revealing several new prominent statistical properties. The distribution theory of concomitants of order statistics from this family is investigated. Besides, some aspects of information measures, namely the Shannon entropy, inaccuracy measure, and Fisher information number, are theoretically and numerically studied. Two bivariate real-world data sets have been analyzed for illustrative purposes, and the performance is quite satisfactory.