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ON THE EVALUATION OF MULTIVARIATE COMPOUND DISTRIBUTIONS WITH CONTINUOUS SEVERITY DISTRIBUTIONS AND SARMANOV'S COUNTING DISTRIBUTION

Published online by Cambridge University Press:  17 January 2018

Maissa Tamraz  and
Raluca Vernic
Maissa Tamraz
Affiliation:
Department of Actuarial Science, University of Lausanne, UNIL-Dorigny 1015 Lausanne, Switzerland E-mail: maissa.tamraz@unil.ch
Raluca Vernic*
Affiliation:
Faculty of Mathematics and Informatics, Ovidius University of Constanta, 124 Mamaia Blvd., 900527 Constanta, Romania Institute for Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania
*
E-mail: rvernic@univ-ovidius.ro
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Abstract

In this paper, we present closed-type formulas for some multivariate compound distributions with multivariate Sarmanov counting distribution and independent Erlang distributed claim sizes. Further on, we also consider a type-II Pareto dependency between the claim sizes of a certain type. The resulting densities rely on the special hypergeometric function, which has the advantage of being implemented in the usual software. We numerically illustrate the applicability and efficiency of such formulas by evaluating a bivariate cumulative distribution function, which is also compared with the similar function obtained by the classical recursion-discretization approach.

Keywords

Multivariate compound modelsarmanov's multivariate discrete distributionErlang distributiontype-II Pareto multivariate distributionhypergeometric function
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 841 - 870
Copyright
Copyright © Astin Bulletin 2018 

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