Moments Characterization of Order 3 Matrix Exponential Distributions

Authors:
András Horváth;Sándor Rácz;Miklós Telek
Affiliations:
Dipartimento di Informatica, University of Torino, Italy;Technical University of Budapest, Hungary;Technical University of Budapest, Hungary
Venue:
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Year:
2009

Citing 3
Cited 2

A minimal representation of Markov arrival processes and a moments matching method

Performance Evaluation
Q-MAM: a tool for solving infinite queues using matrix-analytic methods

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
On the canonical representation of phase type distributions

Performance Evaluation

On moments based Padé approximations of ruin probabilities

Journal of Computational and Applied Mathematics
Rational Automata Networks: A Non-Markovian Modeling Approach

INFORMS Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

The class of order 3 phase type distributions (PH(3)) is known to be a proper subset of the class of order 3 matrix exponential distributions (ME(3)). In this paper we investigate the relation of these two sets for what concerns their moment bounds. To this end we developed a procedure to check if a matrix exponential function of order 3 defines a ME(3) distribution or not. This procedure is based on the time domain analysis of the density function. The proposed procedure requires the numerical solution of a transcendent equation in some cases. The presented moment bounds are based on some unproved conjectures which are verified only by numerical investigations.