We show how to calculate individual terms of the Edgeworth series to approximate the distribution of the Pearson correlation coefficient with the help of a simple Mathematica program. We also demonstrate how to eliminate the corresponding skewness, thus making the approximation substantially more accurate. This leads, in a rather natural way, to deriving a superior (in terms of its accuracy) version of Fisher's z transformation. The code can be easily modified to deal with any sample statistics defined as a function of several sample means, based on a random independent sample from a multivariate distribution.

中文翻译：

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通过 Edgeworth 展开的 Fisher 变换

我们展示了如何在一个简单的 Mathematica 程序的帮助下计算 Edgeworth 系列的各个项以近似 Pearson 相关系数的分布。我们还演示了如何消除相应的偏斜，从而使近似更加准确。这以一种相当自然的方式导致了费舍尔 z 变换的更好（就其准确性而言）版本。基于来自多元分布的随机独立样本，可以轻松修改代码以处理定义为多个样本均值函数的任何样本统计量。