Bayesian inference for double Pareto lognormal queues

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 $dPlN\mathrm{/}M\mathrm{/}1$ and $M\mathrm{/}dPlN\mathrm{/}1$ 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 $Pareto\mathrm{/}M\mathrm{/}1$ system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.