AI 中文总结
研究提出一种类似二项式且具重尾的概率分布，通过两个离散概率质量函数加权平均推导，给出性质并应用于经典数据集，展示了构建统计模型及相关验证适用性的方法。
AI 中文摘要
考虑一种简单的二项分布替代方案，它在尾部放置了更多概率权重。其推导仅需两个离散概率质量函数的加权算术平均值，一个是二项式本身，另一个是此处引入的双均匀分布。推导了一些性质，并讨论了在经典数据集上的应用。该展示可视为关于如何构建统计模型、推导统计性质、通过估计方法将模型拟合到实际数据以及使用统计假设检验要素验证适用性的典范论述。
英文摘要
A simple alternative to the binomial distribution that places more probability weight on the tails is considered. Its derivation only requires the weighted arithmetic mean of two discrete probability mass functions, one being the binomial itself and the other being the bi-uniform introduced here. Some properties are derived, and an application to a classical data set is discussed. The presentation can be seen as an exemplary treatise on how to construct a statistical model, derive statistical properties, fit models to actual data by employing estimation methods, and verify appropriateness by using elements from statistical hypothesis testing.
Comments6 pages, 5 figures
