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Mathematical Problems in Engineering
Volume 2014, Article ID 610907, 13 pages
Research Article

Constructing Matrix Exponential Distributions by Moments and Behavior around Zero

1Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, 10149 Torino, Italy
2Faculty of Computing and Information Technology in Rabigh, King Abdulaziz University, Rabigh, P.O. Box 344, Rabigh 21911, Saudi Arabia

Received 1 September 2014; Accepted 5 December 2014; Published 24 December 2014

Academic Editor: Bo Shen

Copyright © 2014 Alessio Angius et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with moment matching of matrix exponential (ME) distributions used to approximate general probability density functions (pdf). A simple and elegant approach to this problem is applying Padé approximation to the moment generating function of the ME distribution. This approach may, however, fail if the resulting ME function is not a proper probability density function; that is, it assumes negative values. As there is no known, numerically stable method to check the nonnegativity of general ME functions, the applicability of Padé approximation is limited to low-order ME distributions or special cases. In this paper, we show that the Padé approximation can be extended to capture the behavior of the original pdf around zero and this can help to avoid representations with negative values and to have a better approximation of the shape of the original pdf. We show that there exist cases when this extension leads to ME function whose nonnegativity can be verified, while the classical approach results in improper pdf. We apply the ME distributions resulting from the proposed approach in stochastic models and show that they can yield more accurate results.