Time for action – drawing a normal distribution

We can generate random numbers from a normal distribution and visualize their distribution with a histogram (see https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/v/introduction-to-the-normal-distribution). Draw a normal distribution with the following steps:

  1. Generate random numbers for a given sample size using the normal() function from the random NumPy module:
    N=10000
normal_values = np.random.normal(size=N)
  2. Draw the histogram and theoretical PDF with a center value of 0 and standard deviation of 1. Use matplotlib for this purpose:
    _, bins, _ = plt.hist(normal_values, np.sqrt(N), normed=True, lw=1)
sigma = 1
mu = 0
plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ),lw=2)
plt.show()

    In the following diagram, we see the familiar bell curve:

    Time for action – drawing a normal distribution

What just happened?

We visualized the normal distribution using the normal() function from the random NumPy module. We did this by drawing the bell curve and a histogram of randomly generated values (see normaldist.py):

import numpy as np
import matplotlib.pyplot as plt

N=10000

np.random.seed(27)
normal_values = np.random.normal(size=N)
_, bins, _ = plt.hist(normal_values, np.sqrt(N), normed=True, lw=1, label="Histogram")
sigma = 1
mu = 0
plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ), '--', lw=3, label="PDF")
plt.title('Normal distribution')
plt.xlabel('Value')
plt.ylabel('Normalized Frequency')
plt.grid()
plt.legend(loc='best')
plt.show()
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