New SEVERITY Procedure

The new SEVERITY procedure fits models for statistical distributions of the severity (magnitude) of events. A couple of examples of the events typically modeled using the procedure are insurance loss payments and intermittent sales of products.

The SEVERITY procedure is experimental for this release. It provides the following features:

• The magnitude of events can be modeled as a random variable with a continuous parametric probability distribution. The SEVERITY procedure uses the maximum likelihood method to fit multiple specified distributions and identifies the best model based on a specified model selection criterion.

• The SEVERITY procedure is delivered with a set of predefined models for several commonly used distributions. These include the Burr, exponential, gamma, inverse Gaussian, lognormal, Pareto, generalized Pareto, and Weibull distributions.

• The SEVERITY procedure is can be extended to fit any continuous parametric distribution. You can specify the distribution’s model by using a set of functions and subroutines that are defined by using the FCMP procedure. The model must include functions to provide the values of the probability density function (PDF) and the cumulative distribution function (CDF) of the distribution. The model can also optionally include functions or subroutines that provide the distribution’s description, the number of parameters, initial values and bounds for the parameters, the scale parameter transform, and the gradient vector and the Hessian matrix of the PDF and the CDF with respect to the parameters.

• Exogenous variables can be specified for fitting a model that has a scale parameter. The exogenous variables are modeled such that their linear combination affects the scale parameter via a specified link function. The regression coefficients that are associated with the variables in the linear combination are estimated along with the parameters of the distribution. Currently, only the exponential link function is supported.

• Censoring and truncation can be specified for each observed value of the response variable. Global values can also be specified to override the individual values that are associated with each observed value. Currently, only censoring from above (that is, right-censoring) and truncation from below (that is, left-truncation) are allowed.