a reply to http://www.mvkonnik.info/2012/09/normalised-histogram-calculation.html

normalize-histogram.py

#!/usr/bin/env python2

import scipy as sp
import matplotlib.pyplot as plt

SAMPLES=10000
BINS=50

xs = sp.linspace(-5,5,100)
fs = sp.randn(SAMPLES)  # normally distributed samples
pdf = 1.0/sp.sqrt(2*sp.pi)*sp.exp(-0.5*xs**2)

def plothist(heights, bins, name='', color='skyblue'):
    "Plot histogram and PDF from the output of sp.histogram."
    fig = plt.figure()
    p = fig.add_subplot(111)
    p.bar(bins[:-1], heights, width=bins[1]-bins[0], color=color, label=name)
    p.plot(xs, pdf, 'r-', label='pdf')
    p.legend()
    p.set_xlabel("x")
    p.set_ylabel("d")
    p.set_ylim((0,0.5))
    return fig

# method 0: a histogram normalized by SciPy
hs0, bins0 = sp.histogram(fs, bins=BINS, density=True)
fig0 = plothist(hs0, bins0, 'scipy normalization')

# method 1: divide by sum (@virens)
hs, bins = sp.histogram(fs, bins=BINS)
hs1 = hs/float(hs.sum())
fig1 = plothist(hs1, bins, 'div by sum (virens@)')

# method 1b: divide by sum and bin size (fixed)
hs1b = hs/(float(hs.sum())*(bins[1]-bins[0]))
fig1b = plothist(hs1b, bins, 'div by sum AND BIN SIZE')

# method 2: divide by area
hs2 = hs/sp.trapz(hs, x=bins[:-1])
fig2 = plothist(hs2, bins, 'div by area')

fig0.savefig("normhist-scipy.png")
fig1.savefig("normhist-divbysum-bad.png")
fig1b.savefig("normhist-divbysum-fixed.png")
fig2.savefig("normhist-trapz.png")