  Parametric statistical methods play a central role in analyzing risk through
its underlying frequency and severity components. Given the wide availability
of numerical algorithms and high-speed computers, researchers and practitioners
often model these separate (although possibly statistically dependent) random
variables by fitting a large number of parametric probability distributions to
historical data and then comparing goodness-of-fit statistics. However, this
approach is highly susceptible to problems of overfitting because it gives
insufficient weight to fundamental considerations of functional simplicity and
adaptability. To address this shortcoming, we propose a formal mathematical
measure for assessing the versatility of frequency and severity distributions
prior to their application. We then illustrate this approach by computing and
comparing values of the versatility measure for a variety of probability
distributions commonly used in risk analysis.
