Estimation of means and covariances of inverse-Gaussian order statistics

We propose a simulation algorithm to estimate means, variances, and covariances for a set of order statistics from inverse-Gaussian (IG) distributions. Given a set of Monte Carlo data, the algorithm estimates these values simultaneously, Two types of control variates are used: internal uniform and external exponential. Simulation results show that exponential control variates work better, best when the IG skewness is near the exponential skewness value 2. Either type of control variate provides substantial variance reduction for IG distributions that have low skewness.