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Improved Bounds and Simulation Procedures on the Value of the Multivariate Normal Probability Distribution Function

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Abstract

Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function value are given in the paper. The author's variance reduction technique was based on the Bonferroni bounds involving the first two binomial moments only. The new variance reduction technique is adapted to the most refined new bounds developed in the last decade for the estimation the probability of union respectively intersection of events. Numerical test results prove the efficiency of the simulation procedures described in the paper.

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Authors and Affiliations

  1. Operations Research Group, Department of Differential Equations, Institute of Mathematics, Technical University of Budapest, Budapest, Hungary

    Tamás Szántai

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  1. Tamás Szántai
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Szántai, T. Improved Bounds and Simulation Procedures on the Value of the Multivariate Normal Probability Distribution Function. Annals of Operations Research 100, 85–101 (2000). https://doi.org/10.1023/A:1019211000153

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