A General Method for Approximating Tail Probabilities
尾部概率近似的一般方法AI 解读 ↓
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尾部概率近似的一般方法
- 研究问题
- 如何为广泛分布构造容易计算的尾部概率近似，并使近似在极端尾部仍保持较高精度，而无需复杂数值计算？
- 方法与思路
- 作者基于一类微分方程引入新的变换，利用密度函数至少渐近地属于其解集这一性质，构造易求值的尾概率近似函数。
- 材料陈述的贡献
- 摘要称，方法适用于 Pearson 族、逆高斯及若干其他分布，包括标准非中心分布；表格展示了低阶近似的较高精度。
- 阅读关注点
- 应核对变换的原始记号与定义、微分方程条件，以及极端尾部精度采用绝对误差还是相对误差，是否存在统一误差保证。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明，不能推断刊本变化；变换符号排版不清，需查原文，摘要未给出误差数值或金融风险应用。
原文摘要
A new transformation referred to as the G (m) n -transformation is introduced to establish a general methodology for finding functions that are easy to evaluate and give very good approximations to tail probabilities. The transformation is based only on a general class of differential equations that include the specified density function in the solution set, at least asymptotically. As a result this new method applies to a broad class of distributions. Not only is the method general, it is also accurate. Unlike many other approximation methods, the approximation functions produced maintain their high degree of accuracy even in the extreme tails, making them also suitable for extreme tail probability approximation. In this article the method is applied to the Pearson family members, the inverse Gaussian, and the ratio of χ 2 and lognormal that do not belong to the Pearson family. Furthermore, it is applicable in the case of all of the standard noncentral distributions. Tables are included that show the high accuracy of this method even with small values of n (n = 1, 2, 3). In many cases satisfactory approximation functions can be obtained that are sufficiently simple to be calculated on a hand calculator.