How to Use the Log-Normal Distribution in Python

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You can use the lognorm() function from the SciPy library in Python to generate a random variable that follows a log-normal distribution.

The following examples show how to use this function in practice.

How to Generate a Log-Normal Distribution

You can use the following code to generate a random variable that follows a log-normal distribution with μ = 1 and σ = 1:

import math
import numpy as np
from scipy.stats import lognorm

#make this example reproducible
np.random.seed(1)

#generate log-normal distributed random variable with 1000 values
lognorm_values = lognorm.rvs(s=1, scale=math.exp(1), size=1000)

#view first five values
lognorm_values[:5]

array([13.79554017,  1.47438888,  1.60292205,  0.92963   ,  6.45856805])

Note that within the lognorm.rvs() function, s is the standard deviation and the value inside math.exp() is the mean for the log-normal distribution that you’d like to generate.

In this example, we defined the mean to be 1 and the standard deviation to also be 1.

How to Plot a Log-Normal Distribution

We can use the following code to create a histogram of the values for the log-normally distributed random variable we created in the previous example:

import matplotlib.pyplot as plt

#create histogram
plt.hist(lognorm_values, density=True, edgecolor='black')

Matplotlib uses 10 bins in histograms by default, but we can easily increase this number using the bins argument.

For example, we can increase the number of bins to 20:

import matplotlib.pyplot as plt

#create histogram
plt.hist(lognorm_values, density=True, edgecolor='black', bins=20)

The greater the number of bins, the more narrow the bars will be in the histogram.

Related: Three Ways to Adjust Bin Size in Matplotlib Histograms

Additional Resources

The following tutorials explain how to work with other probability distributions in Python:

How to Use the Poisson Distribution in Python
How to Use the Exponential Distribution in Python
How to Use the Uniform Distribution in Python