  Typical risk classification procedure in insurance is consists of a priori
risk classification determined by observable risk characteristics, and a
posteriori risk classification where the premium is adjusted to reflect the
policyholder's claim history. While using the full claim history data is
optimal in a posteriori risk classification procedure, i.e. giving premium
estimators with the minimal variances, some insurance sectors, however, only
use partial information of the claim history for determining the appropriate
premium to charge. Classical examples include that auto insurances premium are
determined by the claim frequency data and workers' compensation insurances are
based on the aggregate severity. The motivation for such practice is to have a
simplified and efficient posteriori risk classification procedure which is
customized to the involved insurance policy. This paper compares the relative
efficiency of the two simplified posteriori risk classifications, i.e. based on
frequency versus severity, and provides the mathematical framework to assist
practitioners in choosing the most appropriate practice.
