The Annals of Applied Statistics

Bayesian inference for double Pareto lognormal queues

Pepa Ramirez-Cobo, Rosa E. Lillo, Simon Wilson, and Michael P. Wiper

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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.

Article information

Ann. Appl. Stat., Volume 4, Number 3 (2010), 1533-1557.

First available in Project Euclid: 18 October 2010

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Heavy tails Laplace transform approximation methods queueing systems Bayesian methods


Ramirez-Cobo, Pepa; Lillo, Rosa E.; Wilson, Simon; Wiper, Michael P. Bayesian inference for double Pareto lognormal queues. Ann. Appl. Stat. 4 (2010), no. 3, 1533--1557. doi:10.1214/10-AOAS336.

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Supplemental materials

  • Supplementary material: Matlab Toolbox. The Matlab toolbox performs Bayesian estimation for the double Pareto Lognormal (dPlN) distribution, and for the queueing systems dPlN / G / 1 and M / dPlN / 1.