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Applications of the Gb2 Family of Probability Distributions in Collective Risk Theory


  • Cummins, J.D.
  • Dionne, G.
  • Maistre, L.


This Article Proposes the Family of Probability Distributions Known As the Generalized Beta of the Second Kind (Gb2) As a Principal Set of Distributions for Modeling Insurance Loss Processes. the Gb2 Family Gamma, Encompasses Many Commonly Used Distributions Such As the Log-Normal, Gamma, and Weibull. It Also Includes Distributions Such As the Burr and Generalized Gamma Which Have Significant Potential for Improving the Distributional Fit in Many Applications Involving Heavy-Tailed Distributions. Most Members of the Gb2 Family Can Be Generated As Mixtures of Well-Known Distributions, Thus Faciliating Theoretical Modeling of Claims From Heterogeneous Populations. an Example Is Presented Which Involves Fitting the Log-Gamma and Log-Burr Distributions to a Sample of Fire Claims. the Results Suggest That Seemingly Slight Differences in Modelling the Tails of Severity Distributions Can Lead to Substantial Differences in Reinsurance Premiums and Quantiles of Simulated Total Claims Distributions.

Suggested Citation

  • Cummins, J.D. & Dionne, G. & Maistre, L., 1987. "Applications of the Gb2 Family of Probability Distributions in Collective Risk Theory," Cahiers de recherche 8719, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:8719

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