### 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 language | English |
---|---|

Title of host publication | Matrix-Analytic Methods in Stochastic Models |

Editors | G. Latouche, V. Ramaswami, J. Sethuraman, K. Sigman, M.S. Squillante, D.D. Yao |

Place of Publication | Heidelberg |

Publisher | Springer Verlag |

Pages | 107-121 |

Number of pages | 256 |

ISBN (Print) | 9781461449089 |

Publication status | Published - 2013 |

### Publication series

Name | Springer Proceedings in Mathematics & Statistics |
---|---|

Number | 27 |

## Fingerprint Dive into the research topics of 'Majorization and extremal PH distributions'. Together they form a unique fingerprint.

## 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). Springer Verlag.