Acyclic Discrete Phase Type Distributions:
Properties and a Parameter Estimation Algorithm
A. Bobbio, A. Horváth, M. Scarpa, M. Telek
Abstract:
This paper provides a detailed study on Discrete Phase Type
(DPH) distributions and its acyclic subclass referred
to as Acyclic DPH (ADPH). Previously not
considered similarities and differences between DPH
and Continuous Phase Type (CPH) distributions are
investigated and minimal representations, called canonical
forms, for the subclass of ADPH distributions are
provided. We investigate the consequences of the recent
result about the minimal coefficient of variation of the
DPH class [Telek, '00] and show that below a given
order (that is a function of the expected value) the minimal
coefficient of variation of the DPH class is always
less than the minimal coefficient of variation of the CPH class. Since all the previously introduced Phase Type
fitting methods were designed for fitting over the CPH class
we provide a DPH fitting method for the first time. The
implementation of the DPH fitting algorithm is found to be
simple and stable. The algorithm is tested over a benchmark
consisting of 10 different continuous distributions. The
error resulted when a continuous distribution sampled in
discrete points is fitted by a DPH is also considered.
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András Horváth, 2008-06-25