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.

翻译：参数化统计方法在通过其基础频率与严重性分量分析风险方面发挥着核心作用。鉴于数值算法与高速计算机的广泛可用性，研究者和实践者通常通过将大量参数化概率分布拟合至历史数据并比较拟合优度统计量，来对这些相互独立（尽管可能存在统计相关性）的随机变量进行建模。然而，这种方法极易产生过拟合问题，因为它未能充分考量函数简洁性与适应性的基本要求。为弥补这一缺陷，我们提出了一种正式的数学度量方法，用于在应用前评估频率分布与严重性分布的多功能性。随后，我们通过计算并比较风险分析中常用的一系列概率分布的多功能性度量值，对该方法进行了示例说明。