An alternative characterization for matrix exponential distributions
Mark Fackrell
Source: Adv. in Appl. Probab. Volume 41, Number 4
(2009), 1005-1022.
Abstract
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.
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1261669583
Digital Object Identifier: doi:10.1239/aap/1261669583
Zentralblatt MATH identifier: 05706687
Mathematical Reviews number (MathSciNet): MR2663233
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