Open Access
September 2010 Bayesian inference for double Pareto lognormal queues
Pepa Ramirez-Cobo, Rosa E. Lillo, Simon Wilson, Michael P. Wiper
Ann. Appl. Stat. 4(3): 1533-1557 (September 2010). DOI: 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 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.


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Pepa Ramirez-Cobo. Rosa E. Lillo. Simon Wilson. Michael P. Wiper. "Bayesian inference for double Pareto lognormal queues." Ann. Appl. Stat. 4 (3) 1533 - 1557, September 2010.


Published: September 2010
First available in Project Euclid: 18 October 2010

zbMATH: 1202.62041
MathSciNet: MR2758340
Digital Object Identifier: 10.1214/10-AOAS336

Keywords: Bayesian methods , heavy tails , Laplace transform approximation methods , queueing systems

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.4 • No. 3 • September 2010
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