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Moment Matching-Based Distribution Fitting with Generalized Hyper-Erlang Distributions

  • Gábor Horváth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7984)

Abstract

This paper describes a novel moment matching based fitting method for phase-type (PH) distributions. A special sub-class of phase-type distributions is introduced for the fitting, called generalized hyper-Erlang distributions. The user has to provide only two parameters: the number of moments to match, and the upper bound for the sum of the multiplicities of the eigenvalues of the distribution, which is related to the maximal size of the resulting PH distribution. Given these two parameters, our method obtains all PH distributions that match the target moments and have a Markovian representation up to the given size. From this set of PH distributions the best one can be selected according to any distance function.

Keywords

Relative Entropy Polynomial System Target Distribution Erlang Distribution Moment Match 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Asmussen, S., Nerman, O., Olsson, M.: Fitting phase-type distributions via the EM algorithm. Scandinavian Journal of Statistics, 419–441 (1996)Google Scholar
  2. 2.
    Bobbio, A., Horváth, A., Telek, M.: Matching three moments with minimal acyclic phase type distributions. Stochastic Models 21(2-3), 303–326 (2005)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Bobbio, A., Telek, M.: A benchmark for PH estimation algorithms: results for Acyclic-PH. Stochastic Models 10(3), 661–677 (1994)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Buchholz, P., Kemper, P., Kriege, J.: Multi-class Markovian arrival processes and their parameter fitting. Performance Evaluation 67(11), 1092–1106 (2010)CrossRefGoogle Scholar
  5. 5.
    Buchholz, P., Telek, M.: Stochastic Petri nets with matrix exponentially distributed firing times. Performance Evaluation 67(12), 1373–1385 (2010)CrossRefGoogle Scholar
  6. 6.
    Casale, G., Zhang, E.Z., Smirni, E.: Interarrival times characterization and fitting for markovian traffic analysis. Numerical Methods for Structured Markov Chains 7461 (2008)Google Scholar
  7. 7.
    El Abdouni Khayari, R., Sadre, R., Haverkort, B.R.: Fitting world-wide web request traces with the EM-algorithm. Performance Evaluation 52(2), 175–191 (2003)CrossRefGoogle Scholar
  8. 8.
    Feldmann, A., Whitt, W.: Fitting mixtures of exponentials to long-tail distributions to analyze network performance models. Performance Evaluation 31(3), 245–279 (1998)CrossRefGoogle Scholar
  9. 9.
    Horváth, A., Telek, M.: PhFit: A general phase-type fitting tool. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 82–91. Springer, Heidelberg (2002)Google Scholar
  10. 10.
    Horváth, G., Telek, M.: On the canonical representation of phase type distributions. Performance Evaluation 66(8), 396–409 (2009)CrossRefGoogle Scholar
  11. 11.
    Johnson, M.A., Taaffe, M.R.: Matching moments to phase distributions: Mixtures of Erlang distributions of common order. Stochastic Models 5(4), 711–743 (1989)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Mocanu, Ş., Commault, C.: Sparse representations of phase-type distributions. Stochastic Models 15(4), 759–778 (1999)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Okamura, H., Dohi, T., Trivedi, K.S.: A refined EM algorithm for PH distributions. Performance Evaluation 68(10), 938–954 (2011)CrossRefGoogle Scholar
  14. 14.
    Telek, M., Heindl, A.: Matching moments for acyclic discrete and continuous phase-type distributions of second order. International Journal of Simulation Systems, Science & Technology 3(3-4) (2002)Google Scholar
  15. 15.
    Thummler, A., Buchholz, P., Telek, M.: A novel approach for fitting probability distributions to real trace data with the EM algorithm. In: Proceedings of the International Conference on Dependable Systems and Networks, DSN 2005, pp. 712–721. IEEE (2005)Google Scholar
  16. 16.
    Verschelde, J.: Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation. ACM Transactions on Mathematical Software (TOMS) 25(2), 251–276 (1999)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Gábor Horváth
    • 1
    • 2
    • 3
  1. 1.Department of Networked Systems and ServicesBudapest University of Technology and EconomicsHungary
  2. 2.MTA-BME Information Systems Research GroupBudapestHungary
  3. 3.Inter-University Center of Telecommunications and InformaticsHungary

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