On Concomitants of Order Statistics from Farlie-Gumbel-Morgenstern Bivariate Lomax Distribution and its Application in Estimation

In this paper, we have dealt with the distribution theory of concomitants of order statistics arising from Farlie-Gumbel-Morgenstern bivariate Lomax distribution. We have discussed the estimation of the parameters associated with the distribution of the variable Y of primary interest, based on the ranked set sample defined by ordering the marginal observations on an auxiliary variable X, when (X,Y) follows a Farlie-Gumbel-Morgenstern bivariate Lomax distribution. When the association parameter and the shape parameter corresponding to Y are known, we have proposed four estimators, viz., an unbiased estimator based on the Stokeschr('39') ranked set sample, the best linear unbiased estimator based on the Stokeschr('39') ranked set sample, the best linear unbiased estimator based on the extreme ranked set sample and the best linear unbiased estimator based on the multistage extreme ranked set sample for the scale parameter of the variable of primary interest. The relative efficiencies of these estimators have also been worked out