Time for action – drawing the lognormal distribution

Let's visualize the lognormal distribution and its PDF with a histogram:

1. Generate random numbers using the normal() function from the random NumPy module:

   N=10000
   lognormal_values = np.random.lognormal(size=N)

2. Draw the histogram and theoretical PDF with a center value of 0 and standard deviation of 1:

   _, bins, _ = plt.hist(lognormal_values, np.sqrt(N), normed=True, lw=1)
   sigma = 1
   mu = 0
   x = np.linspace(min(bins), max(bins), len(bins))
   pdf = np.exp(-(numpy.log(x) - mu)**2 / (2 * sigma**2))/ (x * sigma * np.sqrt(2 * np.pi))
   plt.plot(x, pdf,lw=3)
   plt.show()

   The fit of the histogram and theoretical PDF is excellent, as you can see in the following diagram:

   

What just happened?

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

import numpy as np
import matplotlib...