The Annals of Applied Probability

Phase-Type Distributions and Majorization

Colm Art O'Cinneide

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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.

Article information

Source
Ann. Appl. Probab. Volume 1, Number 2 (1991), 219-227.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1177005935

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoap/1177005935

Mathematical Reviews number (MathSciNet)
MR1102318

Zentralblatt MATH identifier
0729.60069

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60G42: Martingales with discrete parameter

Keywords
Hitting times majorization Markov chains martingales phase-type distributions

Citation

O'Cinneide, Colm Art. Phase-Type Distributions and Majorization. The Annals of Applied Probability 1 (1991), no. 2, 219--227. doi:10.1214/aoap/1177005935. http://projecteuclid.org/euclid.aoap/1177005935.


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