Concomitant of order statistics arising from non-identical independent random vector

In this paper we derive the pdf and cdf of the concomitant of the r-th order statistics arising from a dependent and non-identical random vector (Xi , Yi), i = 1, . . . , n and then present their formulas in a special case when Xi and Yj are independent for i 6= j = 1, . . . , n. We also derive some formulas for the pdf and cdf of concomitant of order statistics arising from a random vector distributed according to an (nested) Archimedean copula. Some explicit formulas for the pdf of concomitant of order statistics was obtained for Clayton and Gumbel families. A numerical example provided for more illustration.