Bayesian inference for double Pareto lognormal queues
Pepa Ramirez-Cobo, Rosa E. Lillo, Simon Wilson, Michael P. Wiper
The Annals of Applied Statistics · 2010 · Volume 4 · Issue 3
Abstract
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 dPlN / M / 1 and M / 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 Pareto / M / 1 system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.
Keywords
Bayesian methods, heavy tails, Laplace transform approximation methods, queueing systems
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