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An alternative characterization for matrix exponential distributions

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  01 July 2016

Mark Fackrell
Mark Fackrell*
Affiliation:
University of Melbourne
*
∗ Postal address: Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia. Email address: [email protected]
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Abstract

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A necessary condition for a rational Laplace–Stieltjes transform to correspond to a matrix exponential distribution is that the pole of maximal real part is real and negative. Given a rational Laplace–Stieltjes transform with such a pole, we present a method to determine whether or not the numerator polynomial admits a transform that corresponds to a matrix exponential distribution. The method relies on the minimization of a continuous function of one variable over the nonnegative real numbers. Using this approach, we give an alternative characterization for all matrix exponential distributions of order three.

Keywords

Matrix exponential distributionrational Laplace–Stieltjes transform

MSC classification

Primary: 60E10: Characteristic functions; other transforms
Secondary: 62E10: Characterization and structure theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 4 , December 2009 , pp. 1005 - 1022
Copyright
Copyright © Applied Probability Trust 2009 

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