Concomitants of order statistics from bivariate phase-type distributions with continuous density functions

Consider (Formula presented.) a random sample from a bivariate random variable. If the sample is ordered according to the Y-variates, then the X-variate paired with the r-th order statistic is called the concomitant of the r-th order statistic (or the r-th concomitant). Given a sample of independent, identically distributed and bivariate phase-type random variables with continuous density function, we provide a procedure to calculate the density function of concomitants of order statistics, and furthermore, we prove that concomitants from this sample are phase-type distributed.