### 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, 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.

Original language | English |
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Number of pages | 8 |

Journal | Stochastic Programming E-Print Series |

Volume | 2006 |

Issue number | 6 |

Publication status | Published - 2006 |

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## Cite this

Olieman, N. J., & van Putten, B. (2006). Estimation method of multivariate exponential probabilities based on a simplex coordinates transform.

*Stochastic Programming E-Print Series*,*2006*(6). http://edoc.hu-berlin.de/series/speps/2006-6/PDF/6.pdf