Paper Info
Title
On the canonical representation of phase type distributions
Abstract
The characterization and the canonical representation of order-n phase type distributions (PH(n)) is an open research problem. This problem is solved for n=2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representations have been introduced for the general PH distribution class so far for n2. In this paper, we summarize the related results for n=3. Starting from these results we provide a canonical representation of the PH(3) class (that is a minimal representation, too) and present a symbolical transformation procedure to obtain the canonical representation based on any (not only Markovian) vector-matrix representation of the distribution. We show that-using the same approach-no symbolical results can be derived for the order-4 PH distributions, thus probably the PH(3) class is the highest order PH class for which a symbolical canonical transformation exists. Using the transformation method to canonical form for PH(3) we numerically evaluate the moment bounds of the PH(3) distribution set, compare it to the order-3 acyclic PH distribution (APH(3)) class, and present other possible applications of the canonical form.
Year
DOI
Venue
2009
10.1016/j.peva.2008.11.002
Perform. Eval.
Keywords
Field
DocType
minimal representation,highest order ph class,vector-matrix representation,phase-type distribution,order-3 acyclic ph distribution,phase type distribution,general ph distribution class,order-4 ph distribution,email address: fghorvath,canonical representation,telekg@hit.bme.hu gabor horvath and miklos,moment bounds,general ph distribution,canonical form,symbolical canonical transformation,canonical transformation,matrix representation
Discrete mathematics,Markov process,Canonical transformation,Canonical form,Phase-type distribution,Equivalence (measure theory),Canonical coordinates,Mathematics
Journal
Volume
Issue
ISSN
66
8
Performance Evaluation
Citations 
PageRank 
References 
14
1.04
2
Authors
2
Name
Order
Citations
PageRank
Gábor Horváth121035.47
Miklós Telek2922102.56