Bayesian Inference for Double Pareto Lognormal Queues Articles uri icon

publication date

  • September 2010

start page

  • 1533

end page

  • 1557


  • 3


  • 4

International Standard Serial Number (ISSN)

  • 1932-6157

Electronic International Standard Serial Number (EISSN)

  • 1941-7330


  • 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.


  • bayesian methods; heavy tails; laplace transform approximation methods; queueing systems