参数风险模型的通用性度量
A Versatility Measure for Parametric Risk Models
AI总结：
本文提出一种数学度量方法，用于评估频率和严重性分布的通用性，以减少过度拟合问题，通过比较不同概率分布的通用性值来改进风险分析。
摘要：
参数统计方法在通过其基础频率和严重性成分分析风险中起着核心作用。鉴于数值算法的广泛可用性和高速计算机的普及，研究者和实践者常通过拟合大量参数概率分布到历史数据并比较拟合优度统计量来建模这些独立（尽管可能统计相关）的随机变量。然而，这种方法容易受到过拟合问题的影响，因为它对功能简单性和适应性等基本考虑因素的重视不足。为了解决这一不足，本文提出了一种正式的数学度量方法，用于在应用之前评估频率和严重性分布的通用性。然后，我们通过计算和比较各种在风险分析中常用概率分布的通用性值来说明这一方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
