Simulating the Integrated Tail Distribution in the Heavy-Tailed Setting

A. Kaasik (Estonia)


conditional Monte Carlo, M/G/1 queue, moments,Pollaczeck-Khinchine formula, simulation, subexponentialdistribution


Let X be a random variable with support on (0, ∞) and a distribution function F(x). Define an integrated tail distribution of F by FI (x) = x 0 (1−F(y))dy/EX and consider a random variable XI with such a distribution. In the paper a simple relation between the moments of X and XI is presented. The result is then extended to a more general case when integrated tail of FI is considered. Simulation of XI is considered in the special case that X is subexponential and novel simulation ideas are discussed when the original distribution is Weibull or log-normal. The results are applied by performing a simulation study using an algorithm by Asmussen and Kroese (presented in [1]) for estimating rare event probabilities with connections to risk and queue processes.

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