For the new bivariate Gompertz distribution, the expression for probability density function (pdf) of rth order statistics and pdf of concomitant arising from rth order statistics are derived. The properties of concomitant arising from the corresponding order statistics are used to derive these results. The exact expression for moment generating function (mgf) of concomitant of order rth statistics is derived. Also, the mean of concomitant arising from rth order statistics is computed using the mgf of concomitant of rth order statistics, and the exact expression for joint density of concomitant of two non-adjacent order statistics are derived.
Kumar, S., Khan, M. J. S., & Kumar, S. (2019). Concomitant of order statistics from new bivariate Gompertz distribution. Journal of Modern Applied Statistical Methods, 18(2), eP2826. doi: 10.22237/jmasm/1604189820