A Canonical Representation of Order 3 Phase Type Distributions

  • Gábor Horváth
  • Miklós Telek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4748)


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 n > 2. In this paper we summarize the related results for n = 3. Starting from these results we recommend a canonical representation of the PH(3) class and present a transformation procedure to obtain the canonical representation based on any (not only Markovian) vector-matrix representation of the distribution.

Using this canonical transformation method we evaluate the moment bounds of the PH(3) distribution set and present the results of our numerical investigations.


Phase Type Distribution Canonical Form Moment Bounds 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Gábor Horváth
    • 1
  • Miklós Telek
    • 1
  1. 1.Department of Telecommunications, Budapest University of Technology and Economics, 1521 BudapestHungary

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