This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide range of applications, as they simply require the assumption of a finite expectation. Even in cases when a particular risk model exists, the new methods provide clarity, security and simplicity. The methodology is applicable to the behavior of financial markets, and the results may be compared to those provided by extreme value theory.

翻译：本文提出了估计超出观测范围的极端概率的方法。这些方法无需模型假设，几乎适用于任何样本量。它们基于次序统计量理论，仅需假设期望有限，因此具有广泛的应用范围。即使在特定风险模型存在的情况下，新方法也能提供清晰性、安全性和简洁性。该方法适用于金融市场行为分析，其结果可与极值理论提供的结果进行比较。