If you specify the SCALEMODEL statement,
then the scale of the distribution depends on the values of regressors.
For a given distribution family, each observation implies a different
scaled version of the distribution. PROC SEVERITY needs to construct
a single representative distribution from all such distributions in
order to compute estimates of CDF and the probability density function
(PDF) that are comparable across different distribution families.
Prior to this release, the representative distribution was constructed
as the weighted mixture of distributions implied by all observations.
For that method, estimation of CDF or PDF for one observation requires
computations, where
denotes the total number of observations. So estimation
of CDF or PDF for all
observations requires
computations, which can dominate the runtime of
PROC SEVERITY even for moderately large values of
. Starting with this release, you can specify the
new DFMIXTURE= option in the SCALEMODEL statement to choose one of
four methods to construct the representative mixture distribution.
The prior method is used when you specify DFMIXTURE=FULL option. The
default method is DFMIXTURE=MEAN, which uses a distribution with scale
equal to the mean of
scale values. It is significantly faster than the
FULL method. The other two methods construct a mixture of
distributions each with one of
scale values, which are either the
-quantiles from the sample of
scale values (DFMIXTURE=QUANTILE) or the scale values
implied by
randomly chosen observations (DFMIXTURE=RANDOM).
For
, the QUANTILE and RANDOM methods can be significantly
faster than the FULL method.