Moment Distributions of Phase Type

Mogens Bladt; Bo Friis Nielsen

Moment Distributions of Phase Type

Mogens Bladt
, Bo Friis Nielsen

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Abstract

In this paper we prove that the class of distributions on the positive reals with a rational Laplace transform, also known as matrix-exponential distributions, is closed under formation of moment distributions. In particular, the results are hence valid for the well known class of phase-type distributions. We construct representations for moment distributions based on a general matrix-exponential distribution which turns out to be a generalization of the moment distributions based on exponential distributions. For moment distributions based on phase{type distributions we find an appropriate alternative representation in terms of sub{intensity matrices. Finally we are able to nd explicit expressions for both the Lorenz curve and the Gini index.

Original language	English

Publisher	Technical University of Denmark, DTU Informatics, Building 321
Publication status	Published - 2009

Series	IMM-Technical Report-2009-12

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abstract = "In this paper we prove that the class of distributions on the positive reals with a rational Laplace transform, also known as matrix-exponential distributions, is closed under formation of moment distributions. In particular, the results are hence valid for the well known class of phase-type distributions. We construct representations for moment distributions based on a general matrix-exponential distribution which turns out to be a generalization of the moment distributions based on exponential distributions. For moment distributions based on phase\{type distributions we find an appropriate alternative representation in terms of sub\{intensity matrices. Finally we are able to nd explicit expressions for both the Lorenz curve and the Gini index.",

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AU - Bladt, Mogens

AU - Nielsen, Bo Friis

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N2 - In this paper we prove that the class of distributions on the positive reals with a rational Laplace transform, also known as matrix-exponential distributions, is closed under formation of moment distributions. In particular, the results are hence valid for the well known class of phase-type distributions. We construct representations for moment distributions based on a general matrix-exponential distribution which turns out to be a generalization of the moment distributions based on exponential distributions. For moment distributions based on phase{type distributions we find an appropriate alternative representation in terms of sub{intensity matrices. Finally we are able to nd explicit expressions for both the Lorenz curve and the Gini index.

AB - In this paper we prove that the class of distributions on the positive reals with a rational Laplace transform, also known as matrix-exponential distributions, is closed under formation of moment distributions. In particular, the results are hence valid for the well known class of phase-type distributions. We construct representations for moment distributions based on a general matrix-exponential distribution which turns out to be a generalization of the moment distributions based on exponential distributions. For moment distributions based on phase{type distributions we find an appropriate alternative representation in terms of sub{intensity matrices. Finally we are able to nd explicit expressions for both the Lorenz curve and the Gini index.