Order statistic exceedance probability sensitivities to alternative model assumptions

Frequency and severity based models form the basis for risk quantification in reinsurance. We provide the mathematical formulation of the order statistics under random sample sizes drawn from a generic discrete frequency distribution, and the canonical distributions (Poisson; negative binomial; binomial). We show how our results can enable practitioners to understand the sensitivity of order statistic exceedance probabilities under varying model assumptions, yielding useful information about reinsurance pricing metrics. We also study the order statistics implied by two generalized frequency distributions (generalized Poisson; Conway-Maxwell-Poisson), pointing out some advantages over the commonly applied canonical distributions in the order statistics context.