The SEVERITY Procedure
- Overview
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Getting Started
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Syntax
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Details
Predefined Distributions Censoring and Truncation Parameter Estimation Method Parameter Initialization Estimating Regression Effects Empirical Distribution Function Estimation Methods Statistics of Fit Defining a Distribution Model with the FCMP Procedure Predefined Utility Functions Custom Objective Functions Input Data Sets Output Data Sets Displayed Output ODS Graphics
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Examples
Defining a Model for Gaussian Distribution Defining a Model for Gaussian Distribution with a Scale Parameter Defining a Model for Mixed-Tail Distributions Estimating Parameters Using Cramér-von Mises Estimator Fitting a Scaled Tweedie Model with Regressors Fitting Distributions to Interval-Censored Data
- References
| DIST Statement |
- DIST distribution-name-or-keyword <(distribution-option) <distribution-name-or-keyword <(distribution-option)>> ...> ;
The DIST statement specifies candidate distributions to be estimated by the SEVERITY procedure. You can specify multiple DIST statements, and each statement can contain one or more distribution specifications.
For your convenience, PROC SEVERITY provides the following 10 different predefined distributions (the name in the parentheses is the name to use in the DIST statement): Burr (BURR), exponential (EXP), gamma (GAMMA), generalized Pareto (GPD), inverse Gaussian or Wald (IGAUSS), lognormal (LOGN), Pareto (PARETO), Tweedie (TWEEDIE), scaled Tweedie (STWEEDIE), and Weibull (WEIBULL). These are described in detail in the section Predefined Distributions.
You can specify any of the predefined distributions or any distribution that you have defined. If the specified distribution is not a predefined distribution, then you must submit the CMPLIB= system option with appropriate libraries before you submit the PROC SEVERITY step to enable the procedure to find the functions associated with your distribution. The predefined distributions are defined in the Sashelp.Svrtdist library. However, you are not required to specify this library in the CMPLIB= system option.
As a convenience, you can also use a shortcut keyword _PREDEFINED_ to indicate that you want to fit all the predefined distributions. Note: The TWEEDIE and STWEEDIE distributions are not included by this keyword. If you want to fit these distributions, then you must specify them explicitly.
If you do not specify any DIST statement, then PROC SEVERITY does not fit any distributions and produces the empirical estimates of the cumulative distribution function provided that you have specified the OUTCDF= option or requested a CDF plot.
- INIT=(name=value ...name=value)
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specifies the initial values to be used for the distribution parameters to start the parameter estimation process. The values must be specified by parameter names. The parameter names must match the names used in the model definition. For example, let a model M’s definition contain a M_PDF function with following signature:
function M_PDF(x, alpha, beta);For this model, the names alpha and beta must be used for the INIT option. The names are case-insensitive. If you do not specify initial values for some parameters in the INIT statement, then a default value of 0.001 is assumed for those parameters. If you specify an incorrect parameter, PROC SEVERITY prints a warning to the SAS log and does not fit the model. All specified values must be nonmissing.
If you are modeling regression effects, then the initial value of the first distribution parameter (alpha in the preceding example) should be the initial base value of the scale parameter or log-transformed scale parameter. More details are provided in the section Estimating Regression Effects.
The use of INIT= option is one of the three methods available for initializing the parameters. You can find more details in the section Parameter Initialization. If none of the initialization methods is used, then PROC SEVERITY initializes all parameters to 0.001.