The transform likelihood ratio method for rare event simulation with heavy tails

Kroese, D. P. and Rubinstein, R. Y. (2004) The transform likelihood ratio method for rare event simulation with heavy tails. Queueing Systems, 46 3-4: 317-351. doi:10.1023/

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Author Kroese, D. P.
Rubinstein, R. Y.
Title The transform likelihood ratio method for rare event simulation with heavy tails
Journal name Queueing Systems   Check publisher's open access policy
ISSN 0257-0130
Publication date 2004
Sub-type Article (original research)
DOI 10.1023/
Open Access Status File (Author Post-print)
Volume 46
Issue 3-4
Start page 317
End page 351
Total pages 35
Editor E. Morozov
R. Serfozo
Place of publication United States
Publisher Springer New York LLC
Collection year 2004
Language eng
Subject 230202 Stochastic Analysis and Modelling
780101 Mathematical sciences
010405 Statistical Theory
010206 Operations Research
Abstract We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.
Keyword Computer Science, Interdisciplinary Applications
Operations Research & Management Science
Heavy Tail Distributions
Rare Events
Importance Sampling
Likelihood Ratio
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

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Created: Wed, 15 Aug 2007, 03:00:10 EST