__Moment Matching Algorithms__

**Brief description of the
algorithms**

**Input:** The input to the algorithm is the first three moments of
a non-negative distribution.

**Output:** The output of the algorithm is the parameters of the phase
type (PH) distributions whose first three moments match the input.

Note that the parameters of a PH distribution is usually specified by
a vector and a matrix, and the format of our output also follows this convention.

### Source code (matlab)

momentmatching.zip

The above file contains the following set of files:

README.txt

matching3PH.m

matching3EC.m

matching3PH2.m

convolutionofPH.m

mixtureofPH.m

isPH2.m

momentofPH.m

**Related documents**

The basic ideas and algorithms are described in

- [PE04c] Takayuki Osogami and Mor Harchol-Balter, "Closed Form Solutions
for Mapping General Distributions to Minimal PH Distributions," submitted
for publication. [closedform.pdf]

You may find more variants of algorithms and other related ideas in

- [TOOLS03b] Takayuki Osogami and Mor Harchol-Balter, "A Closed-form
Solution for Mapping General Distributions to Minimal PH Distributions,"
The 12th International Conference on Modelling
Tools and Techniques for Computer and Communication System Performance
Evaluation (TOOLS 2003), pages 200-217, September 2003. postscript
- Presentation slides (only
for Internet Explorer 5.0 or newer); view presentation slides for [TOOLS03a]
before viewing this.

- [TOOLS03a] Takayuki Osogami and Mor Harchol-Balter, "Necessary
and Sufficient Conditions for Representing General Distributions by Coxians,"
The 12th International Conference on Modelling
Tools and Techniques for Computer and Communication System Performance
Evaluation (TOOLS 2003), pages 182-199, September 2003. postscript
- "Approximating general distributions by minimal PH distributions,"
Workshop
on Quantitative Models for Production and Communication Networks, July
2004.
- Takayuki Osogami and Mor Harchol-Balter, "
A Closed-form Solution for Mapping General Distributions to Minimal PH
Distributions,"
*Technical Report* CMU-CS-03-114 (2003).
- Takayuki Osogami and Mor Harchol-Balter, "
Necessary and Sufficient Conditions for Representing General Distributions
by Coxians,"
*Technical Report* CMU-CS-02-178 (2002).

Takayuki Osogami
Department of Computer Science
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213