The HPSEVERITY Procedure
- Overview
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Getting Started
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Syntax
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DetailsPredefined DistributionsCensoring and TruncationParameter Estimation MethodDetails of Optimization AlgorithmsParameter InitializationEstimating Regression EffectsEmpirical Distribution Function Estimation MethodsStatistics of FitDistributed and Multithreaded ComputationDefining a Severity Distribution Model with the FCMP ProcedurePredefined Utility FunctionsScoring FunctionsCustom Objective FunctionsInput Data SetsOutput Data SetsDisplayed Output
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ExamplesDefining a Model for Gaussian DistributionDefining a Model for the Gaussian Distribution with a Scale ParameterDefining a Model for Mixed-Tail DistributionsFitting a Scaled Tweedie Model with RegressorsFitting Distributions to Interval-Censored DataBenefits of Distributed and Multithreaded ComputingEstimating Parameters Using Cramér-von Mises EstimatorDefining a Finite Mixture Model That Has a Scale ParameterPredicting Mean and Value-at-Risk by Using Scoring Functions
- References
PROC HPSEVERITY writes the OUTEST=, OUTMODELINFO=, and OUTSTAT= data sets when requested by their respective options. The data sets and their contents are described in the following sections.
The OUTEST= data set records the estimates of the model parameters. It also contains estimates of their standard errors and optionally their covariance structure. If you specify BY variables, then the data are organized in BY groups and the data set contains variables that you specify in the BY statement.
If you do not specify the COVOUT option, then the data set contains the following variables:
- _MODEL_
-
identifying name of the distribution model. The observation contains information about this distribution.
- _TYPE_
-
type of the estimates reported in this observation. It can take one of the following two values:
- EST
-
point estimates of model parameters
- STDERR
-
standard error estimates of model parameters
- _STATUS_
-
status of the reported estimates. The possible values are listed in the section _STATUS_ Variable Values.
- <Parameter 1> …<Parameter M>
-
variables, named after the parameters of all candidate distributions, that contain estimates of the respective parameters.
is the cardinality of the union of parameter name sets from all candidate distributions. In an observation, estimates are
populated only for parameters that correspond to the distribution that is indicated by the _MODEL_ variable. If _TYPE_ is
EST, then the estimates are missing if the model does not converge. If _TYPE_ is STDERR, then the estimates are missing if
covariance estimates cannot be obtained.
If you specify regressors, then the estimate that is reported for the first parameter of each distribution is the estimate of the base value of the scale or log-transformed scale parameter. For more information, see the section Estimating Regression Effects.
- <Regressor 1> …<Regressor K>
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If you specify
regressors in the SCALEMODEL statement, then the OUTEST= data set contains variables that are named for each regressor. The variables contain estimates for their respective regression coefficients.
If a regressor is deemed to be linearly dependent on other regressors for a given BY group, then a warning message is written
to the SAS log and a special missing value of .R is written in the respective variable. If _TYPE_ is EST, then the estimates
are missing if the model does not converge. If _TYPE_ is STDERR, then the estimates are missing if covariance estimates cannot
be obtained.
- <Offset Variable>
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If you specify an OFFSET= variable in the SCALEMODEL statement, then the OUTEST= data set contains a variable that is named after the offset variable. If _TYPE_ is EST, then the value of this variable is 1. If _TYPE_ is STDERR, then the value of this variable is a special missing value of .F.
If you specify the COVOUT option in the PROC HPSEVERITY statement, then the OUTEST= data set contains additional observations that contain the estimates of the covariance structure. Given the symmetric nature of the covariance structure, only the lower triangular portion is reported. In addition to the variables listed and described previously, the data set contains the following variables that are either new or have a modified description:
- _TYPE_
-
type of the estimates reported in this observation. For observations that contain rows of the covariance structure, the value is COV.
- _STATUS_
-
status of the reported estimates. For observations that contain rows of the covariance structure, the status is 0 if covariance estimation was successful. If estimation fails, the status is 1 and a single observation is reported with _TYPE_=COV and missing values for all the parameter variables.
- _NAME_
-
name of the parameter for the row of covariance matrix reported in the current observation.
The OUTMODELINFO= data set records the information about each candidate distribution that you specify in the DIST statement. It contains the following variables:
- _MODEL_
-
identifying name of the distribution model. The observation contains information about this distribution.
- _DEPVAR_
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name of the loss variable.
- _DESCRIPTION_
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descriptive name of the model. This has a nonmissing value only if the DESCRIPTION function has been defined for this model.
- _VALID_
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validity of the distribution definition. This has a value of 1 for valid definitions and a value of 0 for invalid definitions. If the definition is invalid, then PROC HPSEVERITY writes the reason for invalidity to the SAS log.
- _PARMNAME
... _PARMNAME -
variables that contain names of parameters of the distribution model, where is the maximum number of parameters across all the specified distribution models. For a given distribution with
parameters, values of variables _PARMNAME
(
) are missing.
The OUTSTAT= data set records statistics of fit and model selection information. If you specify BY variables, then the data are organized in BY groups and the data set contains variables that you specify in the BY statement. The data set contains the following variables:
- _MODEL_
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identifying name of the distribution model. The observation contains information about this distribution.
- _NMODELPARM_
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number of parameters in the distribution.
- _NESTPARM_
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number of estimated parameters. This includes the regression parameters, if you specify any regressors.
- _NOBS_
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number of nonmissing observations used for parameter estimation.
- _STATUS_
-
status of the parameter estimation process for this model. The possible values are listed in the section _STATUS_ Variable Values.
- _SELECTED_
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indicator of the best distribution model. If the value is 1, then this model is the best model for the current BY group according to the specified model selection criterion. This value is missing if the parameter estimation process does not converge for this model.
- Neg2LogLike
-
value of the log likelihood, multiplied by –2, that is attained at the end of the parameter estimation process. This value is missing if the parameter estimation process does not converge for this model.
- AIC
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value of the Akaike’s information criterion (AIC) that is attained at the end of the parameter estimation process. This value is missing if the parameter estimation process does not converge for this model.
- AICC
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value of the corrected Akaike’s information criterion (AICC) that is attained at the end of the parameter estimation process. This value is missing if the parameter estimation process does not converge for this model.
- BIC
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value of the Schwarz Bayesian information criterion (BIC) that is attained at the end of the parameter estimation process. This value is missing if the parameter estimation process does not converge for this model.
- KS
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value of the Kolmogorov-Smirnov (KS) statistic that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
- AD
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value of the Anderson-Darling (AD) statistic that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
- CVM
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value of the Cra
er-von Mises (CvM) statistic that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
The _STATUS_ variable in the OUTEST= and OUTSTAT= data sets contains a value that indicates the status of the parameter estimation process for the respective distribution model. The variable can take the following values in the OUTEST= data set for _TYPE_=EST observations and in the OUTSTAT= data set:
- 0
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The parameter estimation process converged for this model.
- 301
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The parameter estimation process might not have converged for this model because there is no improvement in the objective function value. This might indicate that the initial values of the parameters are optimal, or you can try different convergence criteria in the NLOPTIONS statement.
- 302
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The parameter estimation process might not have converged for this model because the number of iterations exceeded the maximum allowed value. You can try setting a larger value for the MAXITER= options in the NLOPTIONS statement.
- 303
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The parameter estimation process might not have converged for this model because the number of objective function evaluations exceeded the maximum allowed value. You can try setting a larger value for the MAXFUNC= options in the NLOPTIONS statement.
- 304
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The parameter estimation process might not have converged for this model because the time taken by the process exceeded the maximum allowed value. You can try setting a larger value for the MAXTIME= option in the NLOPTIONS statement.
- 400
-
The parameter estimation process did not converge for this model.
The _STATUS_ variable can take the following values in the OUTEST= data set for _TYPE_=STDERR and _TYPE_=COV observations:
- 0
-
The covariance and standard error estimates are available and valid.
- 1
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The covariance and standard error estimates are not available, because the process of computing covariance estimates failed.