The scale factor: a new degree of freedom in phase-type approximation

This paper introduces a unified approach to phase-type approximation in which the discrete and the continuous phase-type models form a common model set. The models of this common set are assigned with a non-negative real parameter, the scale factor. The case when the scale factor is strictly positive results in discrete phase-type distributions and the scale factor represents the time elapsed in one step. If the scale factor is 0, the resulting class is the class of CPH distributions. Applying the above view, it is shown that there is no qualitative difference between the discrete and the CPH models. Based on this unified view of phase-type models one can choose the best phase-type approximation of a stochastic model by optimizing the scale factor.