Zeitschriftenartikel

Integral evaluation using the Delta-squared-distribution: simulation and illustration

Abstract

The Delta-squared-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 Delta-squared ensures an unbiased and efficient estimate of the studied integral regardless of the region it is solved over. The Delta-squared- distribution is also relevant in problems such as separating errors in regression analysis and constructing D-optimal designs in multidimensional regions. Inefficient simulation of Delta-squared prevented the application of the underlying theory in real problems. Ermakov and Missov proposed an algorithm which combines all rejection, inversion, and mixture techniques. Its complexity allows simulating D2 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.