Seaborn distplot y-axis normalisation wrong ticklabels

Question

Just to note, I have already checked this question and this question.

So, I'm using distplot to draw some histograms on separate subplots:

import numpy as np
#import netCDF4 as nc # used to get p0_dict
import matplotlib.pyplot as plt
from collections import OrderedDict
import seaborn.apionly as sns
import cPickle as pickle

''' 
LINK TO PICKLE
https://drive.google.com/file/d/0B8Xks3meeDq0aTFYcTZEZGFFVk0/view?usp=sharing
'''

p0_dict = pickle.load(open('/path/to/pickle/test.dat', 'r'))     

fig = plt.figure(figsize = (15,10))
ax = plt.gca()
j=1

for region, val in p0_dict.iteritems():

    val = np.asarray(val)

    subax = plt.subplot(5,5,j)

    print region

    try:              
        sns.distplot(val, bins=11, hist=True, kde=True, rug=True, 
                     ax = subax, color = 'k', norm_hist=True)

    except Exception as Ex:
        print Ex

    subax.set_title(region)
    subax.set_xlim(0, 1) # the data varies from 0 to 1

    j+=1    

plt.subplots_adjust(left = 0.06, right = 0.99, bottom = 0.07,
                    top = 0.92, wspace = 0.14, hspace = 0.6) 

fig.text(0.5, 0.02, r'$ P(W) = 0,1 $', ha ='center', fontsize = 15)
fig.text(0.02, 0.5, '% occurrence', ha ='center', 
         rotation='vertical', fontsize = 15) 
# obviously I'd multiply the fractional ticklabels by 100 to get 
# the percentage...

plt.show()

What I expect is for the area under the KDE curve to sum to 1, and for the y axis ticklabels to reflect this. However, I get the following:

As you can see, the y axis ticklabels are not in the range [0,1], as would be expected. Turning on/off norm_hist or kde does not change this. For reference, the output with both turned off:

Just to verify:

aus = np.asarray(p0_dict['AUS'])
aus_bins = np.histogram(aus, bins=11)[0]

plt.subplot(121)
plt.hist(aus,11)
plt.subplot(122)
plt.bar(range(0,11),aus_bins.astype(np.float)/np.sum(aus_bins))

plt.show()

The y ticklabels in this case properly reflect those of a normalised histogram.

What am I doing wrong?

Thank you for your help.

Answer 1

The y axis is a density, not a probability. I think you are expecting the normalized histogram to show a probability mass function, where the sum the bar heights equals 1. But that's wrong; the normalization ensures that the sum of the bar heights times the bar widths equals 1. This is what ensures that the normalized histogram is comparable to the kernel density estimate, which is normalized so that the area under the curve is equal to 1.