2024/07/27 by Michael R. Powers, Jiaxin Xu, Powers, Michael R. +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #62E10 #62F07 #Applications (stat.AP) #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Information Theory (cs.IT) #Probability and Risk Models #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2407.19218
openalex publication_date 2024/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.