Estimation method of multivariate exponential probabilities based on a simplex coordinates transform

Abstract

A novel unbiased estimator for estimating the probability mass of a multivariate exponential distribution over a measurable set is introduced and is called the exponential simplex (ES) estimator. For any measurable set and given sample size, the statistical efficiency of the ES estimator is higher than or equal to the statistical efficiency of the well-known Monte Carlo (MC) estimator. For non-radially shaped measurable sets, the ES estimator has a strictly higher statistical efficiency than the MC estimator. For ray-convex sets, such as convex sets, the ES estimator can be expressed in a simple analytical form.