A Versatility Measure for Parametric Risk Models

TL;DR

This paper introduces a formal versatility measure for parametric risk models, helping to evaluate and compare the adaptability of different distributions before application, thus addressing overfitting issues.

Contribution

It proposes a new mathematical measure for assessing the versatility of frequency and severity distributions in risk analysis.

Findings

Versatility measure computed for common risk distributions

Comparison highlights differences in distribution adaptability

Addresses overfitting by emphasizing functional simplicity

Abstract

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.