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The SEVERITY Procedure

The SEVERITY procedure estimates parameters of any arbitrary continuous probability distribution that is used to model magnitude (severity) of a continuous-valued event of interest. Some examples of such events are loss amounts paid by an insurance company and demand of a product as depicted by its sales. PROC SEVERITY is especially useful when the severity of an event does not follow typical distributions, such as the normal distribution, that are often assumed by standard statistical methods.

The following are highlights of the SEVERITY procedure's capabilities:

• provides a default set of probability distribution models that includes the following:
  • Burr
  • exponential
  • gamma
  • generalized Pareto
  • inverse Gaussian (Wald)
  • lognormal
  • Pareto
  • Tweedie
  • Scaled Tweedie
  • Weibull
• enables you to define any arbitrary continuous parametric distribution model and to estimate its parameters
• estimates the model parameters, their standard errors, and their covariance structure by using the maximum likelihood method
• can fit multiple distributions at the same time and choose the best distribution according to a specified selection criterion
• provides the following statistics of fit that can be used as selection criteria:
  • log likelihood
  • Akaike's information criterion
  • corrected Akaike's information criterion
  • Schwarz Bayesian information criterion
  • Kolmogorov-Smirnov statistic
  • Anderson-Darling statistic
  • Cramr-von-Mises statistic
• enables you to fit a distribution model when the severity values are left-truncated or right-censored or both
• enables you to specify a probability of observability for left-truncated data, which is a probability of observing values greater than the left-truncation threshold
• enables you to compute an empirical distribution function (EDF) estimate using Kaplan-Meier's product-limit estimator or Turnbull's estimator
• can model the effect of exogenous or regressor variables on a probability distribution, as long as it has a scale parameter
• enables you to specify your own objective function to be optimized for estimating the parameters of a model
• provides options to control the nonlinear optimization
• obtains separate analyses on observations in groups
• enables you to output data and estimates that can be used in other analyses
• supports ODS Graphics

Documentation

For further details, see the SAS/ETS^® User's Guide

Examples

• A Simple Example of Fitting Predefined Distributions
• An Example with Left-Truncation and Right-Censoring
• An Example of Modeling Regression Effects

• Example 28.1: Defining a Model for Gaussian Distribution
• Example 28.2: Defining a Model for the Gaussian Distribution with a Scale Parameter
• Example 28.3: Defining a Model for Mixed-Tail Distributions
• Example 28.4: Estimating Parameters Using the Cramér–von Mises Estimator
• Example 28.5: Fitting a Scaled Tweedie Model with Regressors
• Example 28.6: Fitting Distributions to Interval-Censored Data
• Example 28.7: Defining a Finite Mixture Model That Has a Scale Parameter
• Example 28.8: Predicting Mean and Value-at-Risk by Using Scoring Functions
• Example 28.9: Scale Regression with Rich Regression Effects