2006-03-09Buch DOI: 10.18452/2980
Estimation method of multivariate exponential probabilities based on a simplex coordinates transform
Olieman, Niels J.
Putten, Bram van
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
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, the standard error of the ES-estimator is at most the standard error of the well known Monte Carlo (MC) estimator. For non-radially shaped measurable sets, the ES-estimator has a strictly smaller standard error than the MC-estimator. For ray-convex sets, such as convex sets, the ES-estimator can be expressed in a simple analytical form.