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Convolutions of multivariate phase-type distributions


  • Berdel, Jasmin
  • Hipp, Christian


This paper is concerned with multivariate phase-type distributions introduced by Assaf et al. (1984). We show that the sum of two independent bivariate vectors each with a bivariate phase-type distribution is again bivariate phase-type and that this is no longer true for higher dimensions. Further, we show that the distribution of the sum over different components of a vector with multivariate phase-type distribution is not necessarily multivariate phase-type either, if the dimension of the components is two or larger.

Suggested Citation

  • Berdel, Jasmin & Hipp, Christian, 2011. "Convolutions of multivariate phase-type distributions," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 374-377, May.
  • Handle: RePEc:eee:insuma:v:48:y:2011:i:3:p:374-377

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    References listed on IDEAS

    1. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
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