Let's visualize the lognormal distribution and its PDF with a histogram:
Generate random numbers using the
normal()
function from therandom
NumPy module:N=10000 lognormal_values = np.random.lognormal(size=N)
Draw the histogram and theoretical PDF with a center value of
0
and standard deviation of1
:_, 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: