python - plotting a histogram on a Log scale with Matplotlib

Question

I have a pandas DataFrame that has the following values in a Series

x = [2, 1, 76, 140, 286, 267, 60, 271, 5, 13, 9, 76, 77, 6, 2, 27, 22, 1, 12, 7, 19, 81, 11, 173, 13, 7, 16, 19, 23, 197, 167, 1]

I was instructed to plot two histograms in a Jupyter notebook with Python 3.6. No sweat right?

x.plot.hist(bins=8)
plt.show()

I chose 8 bins because that looked best to me. I have also been instructed to plot another histogram with the log of x.

x.plot.hist(bins=8)
plt.xscale('log')
plt.show()

This histogram looks TERRIBLE. Am I not doing something right? I've tried fiddling around with the plot, but everything I've tried just seems to make the histogram look even worse. Example:

x.plot(kind='hist', logx=True)

I was not given any instructions other than plot the log of X as a histogram.

I really appreciate any help!!!

For the record, I have imported pandas, numpy, and matplotlib and specified that the plot should be inline.

Answer 1

Specifying bins=8 in the hist call means that the range between the minimum and maximum value is divided equally into 8 bins. What is equal on a linear scale is distorted on a log scale.

What you could do is specify the bins of the histogram such that they are unequal in width in a way that would make them look equal on a logarithmic scale.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

x = [2, 1, 76, 140, 286, 267, 60, 271, 5, 13, 9, 76, 77, 6, 2, 27, 22, 1, 12, 7, 
     19, 81, 11, 173, 13, 7, 16, 19, 23, 197, 167, 1]
x = pd.Series(x)

# histogram on linear scale
plt.subplot(211)
hist, bins, _ = plt.hist(x, bins=8)

# histogram on log scale. 
# Use non-equal bin sizes, such that they look equal on log scale.
logbins = np.logspace(np.log10(bins[0]),np.log10(bins[-1]),len(bins))
plt.subplot(212)
plt.hist(x, bins=logbins)
plt.xscale('log')
plt.show()

Answer 2

Here is one more solution without using a subplot or plotting two things in the same image.

import numpy as np
import matplotlib.pyplot as plt

def plot_loghist(x, bins):
  hist, bins = np.histogram(x, bins=bins)
  logbins = np.logspace(np.log10(bins[0]),np.log10(bins[-1]),len(bins))
  plt.hist(x, bins=logbins)
  plt.xscale('log')

plot_loghist(np.random.rand(200), 10)

Answer 3

plot another histogram with the log of x.

is not the same as plotting x on the logarithmic scale. Plotting the logarithm of x would be

np.log(x).plot.hist(bins=8)
plt.show()

The difference is that the values of x themselves were transformed: we are looking at their logarithm.

This is different from plotting on the logarithmic scale, where we keep x the same but change the way the horizontal axis is marked up (which squeezes the bars to the right, and stretches those to the left).