CCDM Procedure
Parameter Perturbation Analysis
It is important to realize that most of the parameters of the frequency and severity models are estimated and that there is uncertainty associated with the parameter estimates. Any compound distribution estimate that you compute by using these uncertain parameter estimates is inherently uncertain. The aggregate loss sample that you simulate by using the mean estimates of the parameters is just one possible sample from the compound distribution. If information about the uncertainty in parameter estimates is available, then it is recommended that you perform parameter perturbation analysis that generates multiple samples of the compound distribution, in which each sample is simulated by using a set of perturbed parameter estimates. You can use the NPERTURBEDSAMPLES= option in the PROC CCDM statement to specify the number of perturbed samples to be generated. PROC CCDM creates the set of perturbed parameter estimates by making a random draw of the parameter values from their joint probability distribution. If you specify NPERTURBEDSAMPLES=P, then PROC CCDM creates P sets of perturbed parameters, and each set is used to simulate a full aggregate sample. The summary analysis of P such aggregate loss samples results in a set of P estimates for each summary statistic and percentile of the compound distribution. The mean and standard deviation of this set of P estimates quantify the uncertainty that is associated with the compound distribution.
The parameter estimate uncertainty information is available in the form of either the variance-covariance matrix of the parameter estimates or standard errors of the parameter estimates. If the variance-covariance matrix is available and is positive definite, then PROC CCDM assumes that the joint probability distribution of the parameter estimates is a multivariate normal distribution, 
, where the mean vector 
is the set of point parameter estimates and 
is the variance-covariance matrix. If the variance-covariance matrix is not available or is not positive definite, or if you specify the IGNORECOV option, then PROC CCDM assumes that each parameter has a univariate normal distribution, 
, where 
is the point estimate of the parameter and 
is the standard error of the parameter estimate.
Specifying Parameter Uncertainty
If you specify the severity models by using the SEVERITYEST= data table, then the point parameter estimates are expected to be available in the SEVERITYEST= data table in observations for which _TYPE_='EST', the standard errors are expected to be available in the SEVERITYEST= data table in observations for which _TYPE_='STDERR', and the variance-covariance matrix is expected to be available in the SEVERITYEST= data table in observations for which _TYPE_='COV'. When you use the SEVSELECT procedure to create the SEVERITYEST= data table, you need to specify the COVOUT option in the PROC SEVSELECT statement to make the variance-covariance estimates available in the SEVERITYEST= data table.
If you specify the severity models by using the SEVERITYSTORE= item store, then you need to specify the OUTSTORE= option in the PROC SEVSELECT statement to create that item store, which includes the point parameter estimates and standard errors by default. In addition, you need to specify the COVOUT option in the PROC SEVSELECT statement to make the variance-covariance estimates available in the SEVERITYSTORE= item store.
If you specify the frequency model by using the COUNTSTORE= item store, then the uncertainty estimates are available in that item store, because the CNTSELECT procedure always writes the point estimates, standard errors, and variance-covariance matrix of the parameters to the item store.
If you specify the frequency model by using the COUNTMODEL statement, then it is recommended that you use the STDERROR= option to specify the standard error for each parameter.
If you specify an external frequency model by using the EXTERNALCOUNTS statement, then there is no way to specify the uncertainty in the frequency model, so PROC CCDM conducts the perturbation analysis by perturbing only the parameters of the severity model.
Output of Perturbation Analysis
PROC CCDM displays the effect of parameter perturbation on the summary statistics and percentiles of the compound distribution in the ODS tables PerturbedSummary and PerturbedPctlSummary, respectively. For each statistic, the tables report the mean and standard error that PROC CCDM computes by aggregating the statistics from all P perturbed samples. For more information, see the section Displayed Output.
You can specify the OUTSUM statement to write the summary statistics and percentiles of individual perturbed samples to an output data table. You can also specify the PERTURBOUT option in the OUTPUT statement to write all perturbed samples in their entirety to an output data table.
If you specify the ADJUSTEDSEVERITY= option in the PROC CCDM statement, then PROC CCDM performs a separate perturbation analysis for the distribution of each aggregate adjusted loss.