A Normal Approximation for Binomial, F , Beta, and other Common, Related Tail Probabilities, I
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二项、F、贝塔及其他相关常见分布尾概率的正态近似（一）
- 研究问题
- 如何为贝塔分布及二项、F、t 等相关分布的尾概率提供便于计算的正态近似，并评估极端尾部的近似误差？
- 方法与思路
- 作者构造由代数函数和对数组成的近似正态偏差量，提供专用表格、误差图及修正方式，并列出递推关系和连分式。
- 材料陈述的贡献
- 摘要称，新近似在许多极端尾部仍较准确，但对呈或接近 J、U 形的贝塔分布存在例外；图示比较显示其较其他近似更准确。
- 阅读关注点
- 应核对不同分布的参数映射、误差图覆盖范围和尾部误差指标，以及例外情形、修正步骤和超出图示范围的计算方法。
- 阅读边界
- 依据 OpenAlex 索引摘要，稿件版本未注明。准确性是摘要报告，未提供具体误差界；摘要明确将理论与多数证明留给下一篇，不能视为本篇已完整证明。
原文摘要
This paper concerns a new Normal approximation to the beta distribution and its relatives, in particular, the binomial, Pascal, negative binomial, F, t, Poisson, gamma, and chi square distributions. The approximate Normal deviates are expressible in terms of algebraic functions and logarithms, but for desk calculation it is preferable in most cases to use an equivalent expression in terms of a function specially tabulated here. Graphs of the error are provided. They show that the approximation is good even in the extreme tails except for beta distributions which are J or U shaped or nearly so, and they permit correction to obtain still more accuracy. For use beyond the range of the graphs, some standard recursive relations and some classical continued fractions are listed, with some properties of the latter which seem to be partly new. Various Normal approximations are compared, with further graphs. The new approximation appears far more accurate than the others. Everything an ordinary user of the approximation might want to know is included in this paper. The theory behind the approximation and most proofs are postponed to a second paper immediately following this one.