Python – Inverse of Normal Cumulative Distribution Function (CDF)

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Problem Formulation

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

Method 1: scipy.stats.norm.ppf()

In Excel, NORMSINV is the inverse of the CDF of the standard normal distribution.

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In Python’s SciPy library, the ppf() method of the scipy.stats.norm object is the percent point function, which is another name for the quantile function. This ppf() method is the inverse of the cdf() function in SciPy.

  • norm.cdf() is the inverse function of norm.ppf()
  • norm.ppf() is the inverse function of norm.cdf()

You can see this in the following code snippet:

from scipy.stats import norm

print(norm.cdf(norm.ppf(0.5)))
print(norm.ppf(norm.cdf(0.5)))

The output is as follows:

0.5
0.5000000000000001

An alternative is given next:

Method 2: statistics.NormalDist.inv_cdf()

Python 3.8 provides the NormalDist object as part of the statistics module that is included in the standard library. It includes the inverse cumulative distribution function inv_cdf(). To use it, pass the mean (mu) and standard deviation (sigma) into the NormalDist() constructor to adapt it to the concrete normal distribution at hand.

Have a look at the following code:

from statistics import NormalDist

res = NormalDist(mu=1, sigma=0.5).inv_cdf(0.5)
print(res)
# 1.0

A great resource on the topic is given next.

References:

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