The HPSEVERITY Procedure
- Overview
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Getting Started
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Syntax
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DetailsPredefined DistributionsCensoring and TruncationParameter Estimation MethodParameter InitializationEstimating Regression EffectsLevelization of Classification VariablesSpecification and Parameterization of Model 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 OutputODS Graphics
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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 FunctionsScale Regression with Rich Regression Effects
- References
Parameter Initialization
PROC HPSEVERITY enables you to initialize parameters of a model in different ways. A model can have two kinds of parameters: distribution parameters and regression parameters.
The distribution parameters can be initialized by using one of the following three methods:
- INIT= option
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You can use the INIT= option in the DIST statement.
- INEST= or INSTORE= option
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You can use either the INEST= data set or the INSTORE= item store, but not both.
- PARMINIT subroutine
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You can define a dist_PARMINIT subroutine in the distribution model. For more information, see the section Defining a Severity Distribution Model with the FCMP Procedure.
Note that only one of the initialization methods is used. You cannot combine them. They are used in the following order:
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The method that uses the INIT= option takes the highest precedence. If you use the INIT= option to provide an initial value for at least one parameter, then other initialization methods (INEST=, INSTORE=, or PARMINIT) are not used. If you specify initial values for some but not all the parameters by using the INIT= option, then the uninitialized parameters are initialized to the default value of 0.001.
If you use this option and if you specify the regression effects, then the value of the first distribution parameter must be related to the initial value for the base value of the scale or log-transformed scale parameter. For more information, see the section Estimating Regression Effects.
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The method that uses the INEST= data set or INSTORE= item store takes second precedence. If the INEST= data set or INSTORE= item store contains a nonmissing value for even one distribution parameter, then the PARMINIT method is not used and any uninitialized parameters are initialized to the default value of 0.001.
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If none of the distribution parameters are initialized by using the INIT= option, the INEST= data set, or the INSTORE= item store, but the distribution model defines a PARMINIT subroutine, then PROC HPSEVERITY invokes that subroutine with appropriate inputs to initialize the parameters. If the PARMINIT subroutine returns missing values for some parameters, then those parameters are initialized to the default value of 0.001.
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If none of the initialization methods are used, each distribution parameter is initialized to the default value of 0.001.
For more information about regression models and initialization of regression parameters, see the section Estimating Regression Effects.
PARMINIT-Based Parameter Initialization Method and Distributed Data
If you specify a distributed mode of execution for the procedure, then the input data are distributed across the computational nodes. For more information about the distributed computing model, see the section Distributed and Multithreaded Computation. If the PARMINIT subroutine is used for initializing the distribution parameters, then PROC HPSEVERITY invokes that subroutine on each computational node with the data that are local to that node. The EDF estimates that are supplied to the PARMINIT subroutine are also computed using the local data. The initial values of the parameters that are supplied to the optimizer are the average of the local estimates that are computed on each node. This approach works well if the data are distributed randomly across nodes. If you distribute the data on the appliance before you run the procedure (alongside-the-database model), then you should try to make the distribution as random as possible in order to increase the chances of computing good initial values. If you specify a data set that is not distributed before you run the procedure, then PROC HPSEVERITY distributes the data for you by sending the first observation to the first node, the second observation to the second node, and so on. If the order of observations is random, then this method ensures random distribution of data across the computational nodes.