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An alternative characterization for matrix exponential distributions
Published online by Cambridge University Press: 01 July 2016
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.
MSC classification
Secondary:
62E10: Characterization and structure theory
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- General Applied Probability
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- Copyright © Applied Probability Trust 2009
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