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Majorization and Extremal PH Distributions

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Matrix-Analytic Methods in Stochastic Models

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 27))

Abstract

This chapter presents majorization results for PH generators. Based on the majorization results, bounds on the moments and Laplace–Stieltjes transforms of phase-type distributions are found. Exponential distributions and Coxian distributions are identified to be extremal PH distributions with respect to all the moments and Laplace–Stieltjes transforms for certain subsets of PH distributions.

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Acknowledgements

The authors would like to thank reviewers for their valuable comments and suggestions. The authors would also like to thank Mr. Zurun Xu for proofreading the paper.

Author information

Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Qi-Ming He

  2. University of Singapore, Singapore, 119245, Singapore

    Hanqin Zhang

  3. Tilburg University, Tilburg, The Netherlands

    Juan C. Vera

Authors
  1. Qi-Ming He
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  2. Hanqin Zhang
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  3. Juan C. Vera
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Corresponding author

Correspondence to Qi-Ming He .

Editor information

Editors and Affiliations

  1. , Faculté des Sciences, Univ. Libre de Bruxelles, Blvd. du Triomphe, CP 212, Bruxelles, 1050, Belgium

    Guy Latouche

  2. At&T Labs Research, Park Avenue 180, Florham Park, 07932, New Jersey, USA

    Vaidyanathan Ramaswami

  3. , IEOR, Columbia University, West 120th Street 500, New York City, 10027, New York, USA

    Jay Sethuraman

  4. , Dept of Industrial Engineering and OR, Columbia University, 312 Mudd Bldg., New York, 10027, New York, USA

    Karl Sigman

  5. IBM Thomas J. Watson Research Center, Kitchawan Road 1101, Yorktown Heights, 10598, New York, USA

    Mark S. Squillante

  6. , IEOR, Columbia University, West 120th Street 500, New York City, 10027, New York, USA

    David D. Yao

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He, QM., Zhang, H., Vera, J.C. (2013). Majorization and Extremal PH Distributions. In: Latouche, G., Ramaswami, V., Sethuraman, J., Sigman, K., Squillante, M., D. Yao, D. (eds) Matrix-Analytic Methods in Stochastic Models. Springer Proceedings in Mathematics & Statistics, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4909-6_6

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