Tracer une loi normale (gaussienne) avec le module matplotlib de python

Exemple de comment calculer et tracer une loi normale (ou loi gaussienne) avec python et matplotlib en utilisant le module stats de scipy:

from scipy.integrate import quad

import matplotlib.pyplot as plt
import scipy.stats
import numpy as np


x_min = 0.0
x_max = 16.0

mean = 8.0 
std = 2.0

x = np.linspace(x_min, x_max, 100)

y = scipy.stats.norm.pdf(x,mean,std)

plt.plot(x,y, color='coral')

plt.grid()

plt.xlim(x_min,x_max)
plt.ylim(0,0.25)

plt.title('How to plot a normal distribution in python with matplotlib',fontsize=10)

plt.xlabel('x')
plt.ylabel('Normal Distribution')

plt.savefig("normal_distribution.png")
plt.show()

Un autre exemple:

from scipy.integrate import quad

import matplotlib.pyplot as plt
import scipy.stats
import numpy as np


x_min = 0.0
x_max = 16.0

mean = 8.0 
std = 3.0

x = np.linspace(x_min, x_max, 100)

y = scipy.stats.norm.pdf(x,mean,std)

plt.plot(x,y, color='black')

#----------------------------------------------------------------------------------------#
# fill area 1

pt1 = mean + std
plt.plot([pt1 ,pt1 ],[0.0,scipy.stats.norm.pdf(pt1 ,mean, std)], color='black')

pt2 = mean - std
plt.plot([pt2 ,pt2 ],[0.0,scipy.stats.norm.pdf(pt2 ,mean, std)], color='black')

ptx = np.linspace(pt1, pt2, 10)
pty = scipy.stats.norm.pdf(ptx,mean,std)

plt.fill_between(ptx, pty, color='#0b559f', alpha='1.0')

#----------------------------------------------------------------------------------------#
# fill area 2

pt1 = mean + std
plt.plot([pt1 ,pt1 ],[0.0,scipy.stats.norm.pdf(pt1 ,mean, std)], color='black')

pt2 = mean + 2.0 * std
plt.plot([pt2 ,pt2 ],[0.0,scipy.stats.norm.pdf(pt2 ,mean, std)], color='black')

ptx = np.linspace(pt1, pt2, 10)
pty = scipy.stats.norm.pdf(ptx,mean,std)

plt.fill_between(ptx, pty, color='#2b7bba', alpha='1.0')

#----------------------------------------------------------------------------------------#
# fill area 3

pt1 = mean - std
plt.plot([pt1 ,pt1 ],[0.0,scipy.stats.norm.pdf(pt1 ,mean, std)], color='black')

pt2 = mean - 2.0 * std
plt.plot([pt2 ,pt2 ],[0.0,scipy.stats.norm.pdf(pt2 ,mean, std)], color='black')

ptx = np.linspace(pt1, pt2, 10)
pty = scipy.stats.norm.pdf(ptx,mean,std)

plt.fill_between(ptx, pty, color='#2b7bba', alpha='1.0')

#----------------------------------------------------------------------------------------#
# fill area 4

pt1 = mean + 2.0 * std
plt.plot([pt1 ,pt1 ],[0.0,scipy.stats.norm.pdf(pt1 ,mean, std)], color='black')

pt2 = mean + 3.0 * std
plt.plot([pt2 ,pt2 ],[0.0,scipy.stats.norm.pdf(pt2 ,mean, std)], color='black')

ptx = np.linspace(pt1, pt2, 10)
pty = scipy.stats.norm.pdf(ptx,mean,std)

plt.fill_between(ptx, pty, color='#539ecd', alpha='1.0')

#----------------------------------------------------------------------------------------#
# fill area 5

pt1 = mean - 2.0 * std
plt.plot([pt1 ,pt1 ],[0.0,scipy.stats.norm.pdf(pt1 ,mean, std)], color='black')

pt2 = mean - 3.0 * std
plt.plot([pt2 ,pt2 ],[0.0,scipy.stats.norm.pdf(pt2 ,mean, std)], color='black')

ptx = np.linspace(pt1, pt2, 10)
pty = scipy.stats.norm.pdf(ptx,mean,std)

plt.fill_between(ptx, pty, color='#539ecd', alpha='1.0')

#----------------------------------------------------------------------------------------#
# fill area 6

pt1 = mean + 3.0 * std
plt.plot([pt1 ,pt1 ],[0.0,scipy.stats.norm.pdf(pt1 ,mean, std)], color='black')

pt2 = mean + 10.0 *std
plt.plot([pt2 ,pt2 ],[0.0,scipy.stats.norm.pdf(pt2 ,mean, std)], color='black')

ptx = np.linspace(pt1, pt2, 10)
pty = scipy.stats.norm.pdf(ptx,mean,std)

plt.fill_between(ptx, pty, color='#89bedc', alpha='1.0')

#----------------------------------------------------------------------------------------#
# fill area 7

pt1 = mean - 3.0 * std
plt.plot([pt1 ,pt1 ],[0.0,scipy.stats.norm.pdf(pt1 ,mean, std)], color='black')

pt2 = mean - 10.0 * std
plt.plot([pt2 ,pt2 ],[0.0,scipy.stats.norm.pdf(pt2 ,mean, std)], color='black')

ptx = np.linspace(pt1, pt2, 10)
pty = scipy.stats.norm.pdf(ptx,mean,std)

plt.fill_between(ptx, pty, color='#89bedc', alpha='1.0')

#----------------------------------------------------------------------------------------#

plt.grid()

plt.xlim(x_min,x_max)
plt.ylim(0,0.25)

plt.title('How to plot a normal distribution in python with matplotlib',fontsize=10)

plt.xlabel('x')
plt.ylabel('Normal Distribution')

plt.savefig("normal_distribution_2.png")
plt.show()

Références