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in Computational Science & Engineering
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A Fast Simulation Method for the Sum of Subexponential Distributions
Publications
A Fast Simulation Method for the Sum of Subexponential Distributions
Bibliography:
Bibliography
Nadhir Ben Rached, Fatma Benkhelifa, Abla Kammoun, MohamedSlim Alouini, Raul Tempone, A Fast Simulation Method for the Sum of Subexponential Distributions, submitted to arXiv:1406.4689v4, Jun. 2014
Authors:
Nadhir Ben Rached, Fatma Benkhelifa, Abla Kammoun, MohamedSlim Alouini, Raul Tempone
Keywords:
A Fast Simulation Method for the Sum of Subexponential Distributions
Year:
2014
Abstract:
Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a wellknown challenging problem. Closedform expression of the sum distribution is usually intractable and presents an open problem. A crude Monte Carlo (MC) simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive especially when dealing with rare events (i.e events with very small probabilities). Importance Sampling (IS) is an alternative approach which effectively improves the computational efficiency of the MC simulation. In this paper, we develop a general framework based on IS approach for the efficient estimation of the probability that the sum of independent and not necessarily identically distributed heavytailed RVs exceeds a given threshold. The proposed IS approach is based on constructing a new sampling distribution by twisting the hazard rate of the original underlying distribution of each component in the summation. A minmax approach is carried out for the determination of the twisting parameter, for any given threshold. Moreover, using this minmax optimal choice, the estimation of the probability of interest is shown to be asymptotically optimal as the threshold goes to infinity. We also offer some selected simulation results illustrating first the efficiency of the proposed IS approach compared to the naive MC simulation. The nearoptimality of the minmax approach is then numerically analyzed.
ISSN:
2014
http://arxiv.org/abs/1406.4689
No
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