In this article we describe a method for carrying out Bayesian inference for the double
Pareto lognormal (dPlN) distribution which has recently been proposed as a model for
heavy-tailed phenomena. We apply our approach to inference for 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 posses a Laplace transform
in closed form. This difficulty is overcome using some recent approximations for the
Laplace transform for the Pareto/M/1 system. Our procedure is illustrated with
applications in internet traffic analysis and risk theory
