Bayesian inference for double Pareto lognormal queues

Details Bayesian inference for double Pareto lognormal queues Bayesian inference for double Pareto lognormal queues

2010-11-15

arxiv.org/abs/1011.3411v1

Annals of Applied Statistics 2010, Vol. 4, No. 3, 1533-1557

Statistics

Applications

Published in at http://dx.doi.org/10.1214/10-AOAS336 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/10-AOAS336

In this article we describe a method for carrying out Bayesian estimation for the double Pareto lognormal (dPlN) distribution which has been proposed as a model for heavy-tailed phenomena. We apply our approach to estimate the $\mathit{dPlN}/M/1$ and $M/\mathit{dPlN}/1$ queueing systems. These systems cannot be analyzed using standard techniques due to the fact that the dPlN distribution does not possess a Laplace transform in closed form. This difficulty is overcome using some recent approximations for the Laplace transform of the interarrival distribution for the $\mathit{Pareto}/M/1$ system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.

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