A common analytical technique involves using a Coxian distribution to model a general distribution G, where the Coxian distribution agrees with G on the first three moments. This technique is motivated by the analytical tractability of the Coxian distribution. Algorithms for mapping an input distribution G 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 G which are well-represented by an n-stage Coxian distribution, in the sense that the Coxian distribution matches the first three moments of G. 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 n-stage Coxian distribution.

30 pages

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