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On The Evaluation Of Multivariate Compound Distributions With Continuous Severity Distributions And Sarmanov'S Counting Distribution

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  • Tamraz, Maissa
  • Vernic, Raluca

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.

Suggested Citation

  • Tamraz, Maissa & Vernic, Raluca, 2018. "On The Evaluation Of Multivariate Compound Distributions With Continuous Severity Distributions And Sarmanov'S Counting Distribution," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 841-870, May.
    • Handle: RePEc:cup:astinb:v:48:y:2018:i:02:p:841-870_00
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    Cited by:

    1. Catalina Bolancé & Raluca Vernic, 2020. "Frequency and Severity Dependence in the Collective Risk Model: An Approach Based on Sarmanov Distribution," Mathematics, MDPI, vol. 8(9), pages 1-17, August.
    2. Vernic, Raluca & Bolancé, Catalina & Alemany, Ramon, 2022. "Sarmanov distribution for modeling dependence between the frequency and the average severity of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 111-125.

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