论文标题
标准正态分布函数及其可逆的近似值
Approximations for Standard Normal Distribution Function and Its Invertible
论文作者
论文摘要
在本文中，我们根据Tocher的近似介绍了标准正态分布的累积分布函数的新近似值。另外，我们使用两个标准（即最大绝对误差和平均绝对误差）评估新近似值的质量。近似值以封闭形式表示，最大绝对误差为4.43*10^（ - 10），而平均绝对误差为9.62*10^（ - 11）。此外，我们提出了基于polya近似值的标准正态分布的反累积函数的近似值，并将发现的准确性与某些现有近似值进行比较。结果表明，我们的近似值基于上述精度措施超过了其他现有的近似值。
In this paper, we introduce a new approximation of the cumulative distribution function of the standard normal distribution based on Tocher's approximation. Also, we assess the quality of the new approximation using two criteria namely the maximum absolute error and the mean absolute error. The approximation is expressed in closed form and it produces a maximum absolute error of 4.43*10^(-10) while the mean absolute error is 9.62*10^(-11). In addition, we propose an approximation of the inverse cumulative function of the standard normal distribution based on Polya approximation and compare the accuracy of our findings with some of the existing approximations. The results show that our approximations surpass other existing ones based on the aforementioned accuracy measures.
