A Normal Approximation for Binomial, F, Beta, and other Common, Related Tail Probabilities, II
A Normal Approximation for Binomial, F, Beta, and other Common, Related Tail Probabilities, II
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二项式、F、Beta 和其他常见相关尾部概率的正态近似，II
DOI：
10.1080/01621459.1968.10480938
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发表时间：
1968
影响因子：
3.7
通讯作者：
J. Pratt
中科院分区：
文献类型：
--
作者：
J. Pratt
摘要本文讨论了β分布及其相关分布的一种新的正态近似，特别是二项分布、Pascal分布、负二项分布、F分布、t分布、泊松分布、伽玛分布和卡方分布。近似的正态偏差可以用代数函数和对数表示，但对于桌面计算，在大多数情况下，最好使用这里特别列出的函数的等效表达式。给出了误差曲线图。他们表明，除了J形或U形或接近U形的beta分布外，即使在极端的尾部，近似也很好，并且允许修正以获得更高的精度。对于图的范围以外的应用，列出了一些标准递归关系和一些经典的连分式，其中连分式的一些性质似乎是部分新的。用进一步的图比较了各种正态近似。新的近似值似乎比其他近似值精确得多。一个普通用户的一切……
Abstract 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 th...