Efficient simulation of complete and censored samples from common bivariate exponential distributions

Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(X_{i:n},Y_{[i:n]})$$</EquationSource> </InlineEquation> be the vector of the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$i$$</EquationSource> </InlineEquation>th <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$X$$</EquationSource> </InlineEquation>-order statistic and its concomitant observed in a random sample of size <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$n$$</EquationSource> </InlineEquation> where the marginal distribution of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$X$$</EquationSource> </InlineEquation> is absolutely continuous. We describe some general algorithms for simulation of complete and Type II censored samples <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$\{(X_{i:n}, Y_{[i:n]}), 1 \le i \le r \le n\}$$</EquationSource> </InlineEquation> 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. Copyright Springer-Verlag Berlin Heidelberg 2013