HEAVY TAILS, IMPORTANCE SAMPLING AND CROSS–ENTROPY
Copyright policy )HEAVY TAILS, IMPORTANCE SAMPLING AND CROSS–ENTROPY
We consider the problem of estimating P (Y1+ ... +Yn > 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 tool for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y1+ ... +Yn > x,) n-1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some 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/1 and GI/G/1 queues are also discussed.
- University of Queensland Australia
- University of Queensland Australia
- Aarhus University Denmark
- Technion – Israel Institute of Technology Israel
- University of Queensland Australia
Maximum Likelihood, GI/G/1 queue, Statistics & Probability, Subexponential Distribution, Pollaczek-khintchine Formula, Pareto distribution, Algorithmic Complexity, Importance Sampling, Rare Event, Gi/g/1 Queue, Weibull Distribution, 230203 Statistical Theory, 519, random walk, 780101 Mathematical sciences, C1, 010206 Operations Research, 280210 Simulation and Modelling, cross-entropy, Cross-entropy, M/g/1 Queue, maximum likelihood, Pareto Distribution, Pollaczek-Khintchine formula, importance sampling, Random Walk, 230117 Operations Research, Distributions, Weibull distribution, Algorithmic complexity, Simulation, subexponential distribution, rare event
Maximum Likelihood, GI/G/1 queue, Statistics & Probability, Subexponential Distribution, Pollaczek-khintchine Formula, Pareto distribution, Algorithmic Complexity, Importance Sampling, Rare Event, Gi/g/1 Queue, Weibull Distribution, 230203 Statistical Theory, 519, random walk, 780101 Mathematical sciences, C1, 010206 Operations Research, 280210 Simulation and Modelling, cross-entropy, Cross-entropy, M/g/1 Queue, maximum likelihood, Pareto Distribution, Pollaczek-Khintchine formula, importance sampling, Random Walk, 230117 Operations Research, Distributions, Weibull distribution, Algorithmic complexity, Simulation, subexponential distribution, rare event
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