Abstract
Let $$(X_{i:n},Y_{[i:n]})$$ be the vector of the $$i$$ th $$X$$ -order statistic and its concomitant observed in a random sample of size $$n$$ where the marginal distribution of $$X$$ is absolutely continuous. We describe some general algorithms for simulation of complete and Type II censored samples $$\{(X_{i:n}, Y_{[i:n]}), 1 \le i \le r \le n\}$$ from such bivariate distributions. We study in detail several algorithms for simulating complete and censored samples from Downton, Marshall---Olkin, Gumbel (Type I) and Farlie-Gumbel-Morgenstern bivariate exponential distributions. We show that the conditioning method in conjunction with an efficient simulation of exponential order statistics that exploits the independence of spacings provides the best method with substantial savings over the basic method. Efficient simulation is essential for investigating the finite-sample distributional properties of functions of order statistics and their concomitants.
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