Journal article
Multivariate Matrix-Exponential Distributions
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.
Language: | English |
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Publisher: | Informa UK Limited |
Year: | 2010 |
Pages: | 1-26 |
ISSN: | 15324214 and 15326349 |
Types: | Journal article |
DOI: | 10.1080/15326340903517097 |
ORCIDs: | Nielsen, Bo Friis |