# Simulation and Estimation of Extreme Quantiles and Extreme Probabilities

Simulation and Estimation of Extreme Quantiles and Extreme Probabilities Let X be a random vector with distribution μ on ℝ d and Φ be a mapping from ℝ d to ℝ. That mapping acts as a black box, e.g., the result from some computer experiments for which no analytical expression is available. This paper presents an efficient algorithm to estimate a tail probability given a quantile or a quantile given a tail probability. The algorithm improves upon existing multilevel splitting methods and can be analyzed using Poisson process tools that lead to exact description of the distribution of the estimated probabilities and quantiles. The performance of the algorithm is demonstrated in a problem related to digital watermarking. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Simulation and Estimation of Extreme Quantiles and Extreme Probabilities

, Volume 64 (2) – Oct 1, 2011
26 pages

/lp/springer_journal/simulation-and-estimation-of-extreme-quantiles-and-extreme-WLauFTrZAo
Publisher
Springer Journals
Subject
Mathematics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Calculus of Variations and Optimal Control; Optimization; Numerical and Computational Physics; Systems Theory, Control
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-011-9135-z
Publisher site
See Article on Publisher Site

### Abstract

Let X be a random vector with distribution μ on ℝ d and Φ be a mapping from ℝ d to ℝ. That mapping acts as a black box, e.g., the result from some computer experiments for which no analytical expression is available. This paper presents an efficient algorithm to estimate a tail probability given a quantile or a quantile given a tail probability. The algorithm improves upon existing multilevel splitting methods and can be analyzed using Poisson process tools that lead to exact description of the distribution of the estimated probabilities and quantiles. The performance of the algorithm is demonstrated in a problem related to digital watermarking.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2011

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