For the distribution shown below, I want to convert the exponential distribution to a normal distribution. I want to do this is as part of data pre-processing so that the classifier can better interpret the feature (named ipc here).

Distribution of ipc feature

The regular log transformation does not work here because of the (x-axis) spread.

How can I transform this data to a normal distribution?

A related answer has been pointed out in the comment but I am looking for some Python code excerpt as well.


  • $\begingroup$ If those ipc values are discrete then it cannot be done - at least not deterministically. If they are continuous, and you can assume a p.d.f., then it would be possible. Are they discrete (it looks so on the graph)? $\endgroup$ May 12 '17 at 23:03
  • $\begingroup$ I have another metric which is continuous and has an exponential distribution. So how can I convert for that metric? $\endgroup$
    – sandyp
    May 12 '17 at 23:06
  • 1
    $\begingroup$ Related, on Cross Validated: stats.stackexchange.com/questions/154396/… $\endgroup$
    – David Z
    May 12 '17 at 23:15
  • $\begingroup$ @DavidZ Thanks, I actually saw that but was hoping for some code to achieve that. I should probably highlight this requirement in my question as well. $\endgroup$
    – sandyp
    May 13 '17 at 0:00
  • 2
    $\begingroup$ Write it yourself. The inverse normal CDF in that recipe is accessible through what scipy calls the percent point function (ppf). $\endgroup$
    – Emre
    May 13 '17 at 0:08

You can use sklearn.preprocessing.QuantileTransformer (or sklearn.preprocessing.PowerTransformer) which does exactly what you want:

from sklearn.preprocessing import QuantileTransformer
import numpy as np

ey = np.random.exponential(size=100)
qt = QuantileTransformer(output_distribution='normal')
no = qt.fit_transform(ey.reshape(-1, 1))

You can plot histograms to compare "before" vs "after":

# Plot histograms to see before vs after.
import matplotlib.pyplot as plt
%matplotlib inline 
plt.subplot(2, 2, 1)
plt.hist(ey, bins='auto')
plt.subplot(2, 2, 2)
plt.hist(no, bins='auto')

enter image description here

The advantage of this approach is that it will also work for other input distributions, not only exponential.


The following code works:

import scipy
import numpy as np

ey = np.random.exponential(size=100)
cdfy = scipy.stats.expon.cdf(np.sort(ey))
invcdf = scipy.stats.norm.ppf(cdfy) # a normal distribution

Hope this helps


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