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We extend the construction principle of multivariate phase-type distributionsto establish an analytically tractable class of heavy-tailed multivariaterandom variables whose marginal distributions are of Mittag-Leffler type witharbitrary index of regular variation. The construction can essentially be seenas allowing a scalar parameter to become matrix-valued. The class ofdistributions is shown to be dense among all multivariate positive randomvariables and hence provides a versatile candidate for the modelling ofheavy-tailed, but tail-independent, risks in various fields of application.

Multivariate Matrix Mittag--Leffler distributions