**Andrea Bobbio, András Horváth, Miklós Telek **

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 Continuous phase-type
distributions. Applying the above view, it is shown that there is
no qualitative difference between the discrete and the continuous
phase-type 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.

**Keywords**: Discrete and Continuous Phase type distributions, Phase
type expansion, approximate analysis.