Moments characterization of order 3 matrix exponential distributions

András Horváth, Sándor Rácz, Miklós Telek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationAnalytical and Stochastic Modeling Techniques and Applications - 16th International Conference, ASMTA 2009, Proceedings
Pages174-188
Number of pages15
DOIs
Publication statusPublished - Aug 21 2009
Event16th International Conference on Analytical and Stochastic Modeling Techniques and Applications, ASMTA 2009 - Madrid, Spain
Duration: Jun 9 2009Jun 12 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5513 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other16th International Conference on Analytical and Stochastic Modeling Techniques and Applications, ASMTA 2009
CountrySpain
CityMadrid
Period6/9/096/12/09

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Keywords

  • Matrix exponential distributions
  • Moment bounds
  • Phase type distributions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Horváth, A., Rácz, S., & Telek, M. (2009). Moments characterization of order 3 matrix exponential distributions. In Analytical and Stochastic Modeling Techniques and Applications - 16th International Conference, ASMTA 2009, Proceedings (pp. 174-188). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5513 LNCS). https://doi.org/10.1007/978-3-642-02205-0_13