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May, 1991 Phase-Type Distributions and Majorization
Colm Art O'Cinneide
Ann. Appl. Probab. 1(2): 219-227 (May, 1991). DOI: 10.1214/aoap/1177005935

Abstract

Aldous and Shepp recently proved that the Erlang distribution of a given order is the least variable phase-type distribution of that order, in the sense of minimizing the coefficient of variation. Here we prove that it is also least variable in the sense of majorization. We give an example showing that the result does not extend in the obvious way to general distributions with rational transforms and this suggests that the inequality hinges on the Markov property.

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Colm Art O'Cinneide. "Phase-Type Distributions and Majorization." Ann. Appl. Probab. 1 (2) 219 - 227, May, 1991. https://doi.org/10.1214/aoap/1177005935

Information

Published: May, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0729.60069
MathSciNet: MR1102318
Digital Object Identifier: 10.1214/aoap/1177005935

Subjects:
Primary: 60J27
Secondary: 60G42

Keywords: hitting times , majorization , Markov chains , Martingales , phase-type distributions

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.1 • No. 2 • May, 1991
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