Background

A common analytical technique involves using a Coxian distribution to model a general distribution, where the Coxian distribution agrees with on the first three moments. This technique is motivated by the analytical tractability of the Coxian distribution. Algorithms for mapping an input distribution to a Coxian distribution largely hinge on knowing a priori the necessary and sufficient number of stages in the representative Coxian distribution. In this paper, we formally characterize the set of distributions which are well-represented by an-stage Coxian distribution, in the sense that the Coxian distribution matches the first three moments of. We also discuss a few common, practical examples. Lastly, we derive a partial characterization of the set of busy period durations which are well-represented by an-stage Coxian distribution