How to draw histograms under a curve?

Question

Suppose we have a function (like pdf of a normal distribution), and we want to approximate it with histograms under the function. I wanna specify the number of bins and draw histograms under the curve. How is it possible to do in Python? For example, a graph like below, but all spikes are under the curve, and the number of bins is a parameter.

Answer 1

You can use the pdf to decide the heights of the bars:

from scipy.stats import norm
import numpy as np
N = 20
x = np.linspace(norm.ppf([0.001, 0.999]), N)
y = norm.pdf(x)

Each center of a bar will be just as high as the pdf, so the bars will cut the curve. To only touch the curve, one could calculate the pdf at the lowest point, being x + width/2 for positive points. As the pdf is symmetric, abs can be used to create a single expression for both positive and negative x-values.

Here is an animation created via the celluloid library.

import matplotlib.pyplot as plt
import numpy as np
import scipy
from scipy.stats import norm
from celluloid import Camera

fig, ax = plt.subplots(figsize=(8, 2))
fig.subplots_adjust(bottom=0.15, left=0.1, right=0.97)
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.spines['bottom'].set_visible(False)
camera = Camera(fig)
x0, x1 = norm.ppf([0.001, 0.999])
x_pdf = np.linspace(x0, x1, 1000)
y_pdf = norm.pdf(x_pdf)
for N in range(10, 80):
    ax.plot(x_pdf, y_pdf, 'r', lw=2)
    x_bar = np.linspace(x0, x1, N)
    width = x_bar[1]-x_bar[0]
    y_bar = norm.pdf(np.abs(x_bar) + width/2)
    ax.bar(x_bar, y_bar, width=width, fc='DeepSkyBlue', ec='k')
    ax.margins(x=0)
    ax.set_ylabel('probability density')
    camera.snap()
animation = camera.animate(interval=600)
animation.save('gaussian_histogram.gif')
plt.show()

PS: Here is a list of related questions (collected by @TrentonMcKinney), where you can find additional explanation and ideas:

• How to add a standard normal pdf over a seaborn histogram
• Fitting a Normal distribution to 1D data
• How do I draw a histogram for a normal distribution using python matplotlib?
• How to plot normal distribution