A Saddle Point Approximation for Certain Multivariate Tail Probabilities
- 1 July 1998
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 19 (4) , 1234-1244
- https://doi.org/10.1137/s1064827594277338
Abstract
We consider the problem of computing the probability of a union of a large number of tail events. This multivariate probability is intractable, so we propose a bound based on univariate and bivariate marginal probabilities, which in turn we approximate by the saddle point method and a correction for skewness. We use this approach to approximate a reliability index for power systems. Our numerical results indicate that this deterministic bound is also an accurate estimate and that it is more efficient than direct Monte Carlo.Keywords
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