Densities for Random Balanced Sampling

A random balanced sample (RBS) is a multivariate distribution with n components Formula Not Shown , each uniformly distributed on Formula Not Shown , such that the sum of these components is precisely 0. The corresponding vectors Formula Not Shown lie in an Formula Not Shown -dimensional polytope Formula Not Shown . We present new methods for the construction of such RBS via densities over Formula Not Shown and these apply for arbitrary n. While simple densities had been known previously for small values of n (namely 2,3, and 4), for larger n the known distributions with large support were fractal distributions (with fractal dimension asymptotic to n as Formula Not Shown ). Applications of RBS distributions include sampling with antithetic coupling to reduce variance, and the isolation of nonlinearities. We also show that the previously known densities (for Formula Not Shown ) are in fact the only solutions in a natural and very large class of potential RBS densities. This finding clarifies the need for new methods, such as those presented here