Plot a histogram such that the total area of the histogram equals 1 (density)

Question

This is a follow-up question to this answer. I'm trying to plot normed histogram, but instead of getting 1 as maximum value on y axis, I'm getting different numbers.

For array k=(1,4,3,1)

 import numpy as np   def plotGraph():         import matplotlib.pyplot as plt          k=(1,4,3,1)      plt.hist(k, normed=1)      from numpy import *     plt.xticks( arange(10) ) # 10 ticks on x axis      plt.show()        plotGraph() 

I get this histogram, that doesn't look like normed.

For a different array k=(3,3,3,3)

 import numpy as np   def plotGraph():         import matplotlib.pyplot as plt          k=(3,3,3,3)      plt.hist(k, normed=1)      from numpy import *     plt.xticks( arange(10) ) # 10 ticks on x axis      plt.show()        plotGraph() 

I get this histogram with max y-value is 10.

For different k I get different max value of y even though normed=1 or normed=True.

Why the normalization (if it works) changes based on the data and how can I make maximum value of y equals to 1?

UPDATE:

I am trying to implement Carsten König answer from plotting histograms whose bar heights sum to 1 in matplotlib and getting very weird result:

import numpy as np  def plotGraph():      import matplotlib.pyplot as plt      k=(1,4,3,1)      weights = np.ones_like(k)/len(k)     plt.hist(k, weights=weights)      from numpy import *     plt.xticks( arange(10) ) # 10 ticks on x axis      plt.show()    plotGraph() 

Result:

What am I doing wrong?

Answer 1

When plotting a normalized histogram, the area under the curve should sum to 1, not the height.

In [44]:  import matplotlib.pyplot as plt k=(3,3,3,3) x, bins, p=plt.hist(k, density=True)  # used to be normed=True in older versions from numpy import * plt.xticks( arange(10) ) # 10 ticks on x axis plt.show()   In [45]:  print bins [ 2.5  2.6  2.7  2.8  2.9  3.   3.1  3.2  3.3  3.4  3.5] 

Here, this example, the bin width is 0.1, the area underneath the curve sums up to one (0.1*10).

x stores the height for each bins. p stores each of those individual bins objects (actually, they are patches. So we just sum up x and modify the height of each bin object.

To have the sum of height to be 1, add the following before plt.show():

for item in p:     item.set_height(item.get_height()/sum(x)) 

Answer 2

You could use the solution outlined here:

weights = np.ones_like(myarray)/float(len(myarray)) plt.hist(myarray, weights=weights)