Simulation and Estimation of Extreme Quantiles and Extreme Probabilities

@article{Guyader2011SimulationAE,
  title={Simulation and Estimation of Extreme Quantiles and Extreme Probabilities},
  author={Arnaud Guyader and Nicolas W. Hengartner and E. Matzner-L{\o}ber},
  journal={Applied Mathematics & Optimization},
  year={2011},
  volume={64},
  pages={171-196}
}
Let X be a random vector with distribution μ on ℝd and Φ be a mapping from ℝd 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… CONTINUE READING

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