The Δ2-distribution is a multivariate distribution, which plays an important role in variance reduction of Monte Carlo integral evaluation. Selecting the nodes of random cubature formulae according to Δ2 ensures an unbiased and efficient estimate of the studied integral regardless of the region it is solved over. The Δ2 distribution is also relevant in problems such as separating errors in regression analysis and constructing D-optimal designs in multidimensional regions. Inefficient simulation of Δ2 prevented the application of the underlying theory in real problems. Ermakov and Missov [S.M. Ermakov and T.I. Missov, On Simulation of the Δ2-distribution. Vestnik St. Petersburg University, issue 4 (2005), 123–140.], proposed an algorithm which combines all rejection, inversion, and mixture techniques. Its complexity allows simulating Δ2 vectors of big lengths. Moreover, it works in the most general settings of the problem of integral evaluation. This article presents a modification of the simulation algorithm as well as its illustration for a popular integral in Reliability Theory.
Copyright 2005, Walter de Gruyter
