Multivariate Matrix-Exponential Distributions

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In this article we consider the distributions of non-negative random vectors with a joint rational Laplace transform, i.e., a fraction between two multi-dimensional polynomials. These distributions are in the univariate case known as matrix-exponential distributions, since their densities can be written as linear combinations of the elements in the exponential of a matrix. For this reason we shall refer to multivariate distributions with rational Laplace transform as multivariate matrix-exponential distributions (MVME). The marginal distributions of an MVME are univariate matrix-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem for the multivariate normal distribution. However, the proof is different and involves theory for rational function based on continued fractions and Hankel determinants.
Original languageEnglish
JournalStochastic Models
Volume26
Issue number1
Pages (from-to)1-26
ISSN1532-6349
DOIs
Publication statusPublished - 2010
CitationsWeb of Science® Times Cited: No match on DOI

    Research areas

  • Continued fractions, Hankel matrices, Multivariate phase-type distribution, Multivariate matrix-exponential
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