Introduction

Distribution of the Severity

The SEVERITY procedure estimates parameters of any probability distribution that is used to model the magnitude (severity) of a continuous-valued event of interest. The SEVERITY procedure includes the following features:

  • parameter estimation of predefined distribution models, including the following:

    • Burr distribution

    • exponential distribution

    • gamma distribution

    • generalized Pareto distribution

    • inverse Gaussian (Wald) distribution

    • lognormal distribution

    • Pareto distribution

    • Tweedie distribution

    • Weibull distribution

  • parameter estimation of arbitrarily defined parametric distribution models

  • fitting distributions to data by either truncation or censoring

  • group estimation

  • several fit statistics, including the following:

    • log likelihood

    • Akaike’s information criterion (AIC)

    • corrected Akaike’s information criterion (AICC)

    • Schwarz Bayesian information criterion (BIC)

    • Kolmogorov-Smirnov statistic (KS)

    • Anderson-Darling statistic (AD)

    • Cramér–von Mises statistic (CvM)

  • regression effects

  • scoring functions

  • multithreaded computation

  • ability to specify the objective function for optimization

  • plots of the estimated cumulative distribution function (CDF), the estimated empirical distribution function (EDF), and the estimated probability density function (PDF)

Last updated: June 19, 2025