Heavy tails, importance sampling and cross-entropy

被引：23

作者：

Asmussen, S

Kroese, DP

Rubinstein, RY

机构：

[1] Aarhus Univ, Dept Math Sci, Dept Theoret Stat, DK-8000 Aarhus C, Denmark

[2] Univ Queensland, Dept Math, Brisbane, Qld 4072, Australia

[3] Technion Israel Inst Technol, Fac Ind Engn & Management, IL-32000 Haifa, Israel

来源：

STOCHASTIC MODELS | 2005年 / 21卷 / 01期

基金：

以色列科学基金会;

关键词：

algorithmic complexity; cross-entropy; GI/G/1; queue; importance sampling; maximum likelihood; M/G/1; Pareto distribution; Pollaczek-Khintchine formula; random walk; rare event; subexponential distribution; Weibull distribution;

D O I：

10.1081/STM-200046472

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the problem of estimating P(Yi + (...) + Y-n > x) by importance sampling when the Yi are i.i.d. and heavy-tailed. The idea is to exploit the cross-entropy method as a toot for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y-1 + (...) + Y-n > x), n - 1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some specific parametric examples (Pareto and Weibull) how this leads to precise answers which, as demonstrated numerically, are close to being variance minimal within the parametric class under consideration. Related problems for M/G/l and GI/G/l queues are also discussed.

引用

页码：57 / 76

页数：20

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