Logistic distribution

This distribution is similar to the normal distribution, but with the morphological difference of having a more elongated tail. The main importance of this distribution lies in its cumulative distribution function (CDF), which we will be using in the following chapters, and will certainly look familiar.

Let's first represent the base distribution by using the following code snippet:

    import matplotlib.pyplot as plt #Import the plot library 
    import numpy as np 
    mu=0.5 
    sigma=0.5 
    distro2 = np.random.logistic(mu, sigma, 10000) 
    plt.hist(distro2, 50, normed=True) 
    distro = np.random.normal(mu, sigma, 10000) 
    plt.hist(distro, 50, normed=True) 
    plt.show() 

Take a look at the following graph:

Then, as mentioned before, let's compute the CDF of the logistic distribution so that you will see a very familiar figure, the sigmoid curve, which we will see again when we review neural network activation functions:

    plt.figure() 
    logistic_cumulative = np.random.logistic(mu, sigma, 10000)/0.02 
    plt.hist(logistic_cumulative, 50, normed=1, cumulative=True) 
    plt.show() 

Take a look at the following graph: