  Every probability distribution can be approximated up to a given precision by
a phase-type distribution, i.e. a distribution encoded by a continuous time
Markov chain (CTMC). However, an excessive number of states in the
corresponding CTMC is needed for some standard distributions, in particular
most distributions with regions of zero density such as uniform or shifted
distributions. Addressing this class of distributions, we suggest an
alternative representation by CTMC extended with discrete-time transitions.
Using discrete-time transitions we split the density function into multiple
intervals. Within each interval, we then approximate the density with standard
phase-type fitting. We provide an experimental evidence that our method
requires only a moderate number of states to approximate such distributions
with regions of zero density. Furthermore, the usage of CTMC with discrete-time
transitions is supported by a number of techniques for their analysis. Thus,
our results promise an efficient approach to the transient analysis of a class
of non-Markovian models.
