Majorization and extremal PH distributions

Q.M. He, H. Zhang, J.C. Vera

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

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.
Original languageEnglish
Title of host publicationMatrix-Analytic Methods in Stochastic Models
EditorsG. Latouche, V. Ramaswami, J. Sethuraman, K. Sigman, M.S. Squillante, D.D. Yao
Place of PublicationHeidelberg
PublisherSpringer Verlag
Pages107-121
Number of pages256
ISBN (Print)9781461449089
Publication statusPublished - 2013

Publication series

NameSpringer Proceedings in Mathematics & Statistics
Number27

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Majorization
Transform
Moment
Phase-type Distribution
Exponential distribution
Generator
Subset

Cite this

He, Q. M., Zhang, H., & Vera, J. C. (2013). Majorization and extremal PH distributions. In G. Latouche, V. Ramaswami, J. Sethuraman, K. Sigman, M. S. Squillante, & D. D. Yao (Eds.), Matrix-Analytic Methods in Stochastic Models (pp. 107-121). (Springer Proceedings in Mathematics & Statistics; No. 27). Heidelberg: Springer Verlag.
He, Q.M. ; Zhang, H. ; Vera, J.C. / Majorization and extremal PH distributions. Matrix-Analytic Methods in Stochastic Models. editor / G. Latouche ; V. Ramaswami ; J. Sethuraman ; K. Sigman ; M.S. Squillante ; D.D. Yao. Heidelberg : Springer Verlag, 2013. pp. 107-121 (Springer Proceedings in Mathematics & Statistics; 27).
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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.",
author = "Q.M. He and H. Zhang and J.C. Vera",
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He, QM, Zhang, H & Vera, JC 2013, Majorization and extremal PH distributions. in G Latouche, V Ramaswami, J Sethuraman, K Sigman, MS Squillante & DD Yao (eds), Matrix-Analytic Methods in Stochastic Models. Springer Proceedings in Mathematics & Statistics, no. 27, Springer Verlag, Heidelberg, pp. 107-121.

Majorization and extremal PH distributions. / He, Q.M.; Zhang, H.; Vera, J.C.

Matrix-Analytic Methods in Stochastic Models. ed. / G. Latouche; V. Ramaswami; J. Sethuraman; K. Sigman; M.S. Squillante; D.D. Yao. Heidelberg : Springer Verlag, 2013. p. 107-121 (Springer Proceedings in Mathematics & Statistics; No. 27).

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

TY - CHAP

T1 - Majorization and extremal PH distributions

AU - He, Q.M.

AU - Zhang, H.

AU - Vera, J.C.

N1 - Pagination: 256

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

M3 - Chapter

SN - 9781461449089

T3 - Springer Proceedings in Mathematics & Statistics

SP - 107

EP - 121

BT - Matrix-Analytic Methods in Stochastic Models

A2 - Latouche, G.

A2 - Ramaswami, V.

A2 - Sethuraman, J.

A2 - Sigman, K.

A2 - Squillante, M.S.

A2 - Yao, D.D.

PB - Springer Verlag

CY - Heidelberg

ER -

He QM, Zhang H, Vera JC. Majorization and extremal PH distributions. In Latouche G, Ramaswami V, Sethuraman J, Sigman K, Squillante MS, Yao DD, editors, Matrix-Analytic Methods in Stochastic Models. Heidelberg: Springer Verlag. 2013. p. 107-121. (Springer Proceedings in Mathematics & Statistics; 27).