如何计算python中正态累积分布函数的倒数? [英] How to calculate the inverse of the normal cumulative distribution function in python?

问题描述

如何在 Python 中计算正态分布的累积分布函数 (CDF) 的倒数?

How do I calculate the inverse of the cumulative distribution function (CDF) of the normal distribution in Python?

我应该使用哪个库?可能是scipy?

Which library should I use? Possibly scipy?

推荐答案

NORMSINV(在注释)是标准正态分布的 CDF 的倒数.使用 scipy，您可以使用 scipy.stats.norm 对象.首字母缩略词 ppf 代表 百分比点函数，这是分位数函数的另一个名称.

NORMSINV (mentioned in a comment) is the inverse of the CDF of the standard normal distribution. Using scipy, you can compute this with the ppf method of the scipy.stats.norm object. The acronym ppf stands for percent point function, which is another name for the quantile function.

In [20]: from scipy.stats import norm

In [21]: norm.ppf(0.95)
Out[21]: 1.6448536269514722

检查它是否是 CDF 的倒数:

Check that it is the inverse of the CDF:

In [34]: norm.cdf(norm.ppf(0.95))
Out[34]: 0.94999999999999996

默认情况下，norm.ppf 使用 mean=0 和 stddev=1，这是标准"正态分布.您可以通过分别指定 loc 和 scale 参数来使用不同的均值和标准差.

By default, norm.ppf uses mean=0 and stddev=1, which is the "standard" normal distribution. You can use a different mean and standard deviation by specifying the loc and scale arguments, respectively.

In [35]: norm.ppf(0.95, loc=10, scale=2)
Out[35]: 13.289707253902945

如果您查看 scipy.stats.norm 的源代码，您会发现 ppf 方法最终调用了 scipy.special.ndtri.因此，要计算标准正态分布的 CDF 的倒数，您可以直接使用该函数:

If you look at the source code for scipy.stats.norm, you'll find that the ppf method ultimately calls scipy.special.ndtri. So to compute the inverse of the CDF of the standard normal distribution, you could use that function directly:

In [43]: from scipy.special import ndtri

In [44]: ndtri(0.95)
Out[44]: 1.6448536269514722

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