Uniform distribution

Let's start off with a really simple example: uniform distribution. A uniform distribution just means there's a flat constant probability of a value occurring within a given range.

import numpy as np 
Import matplotlib.pyplot as plt 
 
values = np.random.uniform(-10.0, 10.0, 100000) 
plt.hist(values, 50) 
plt.show() 

So we can create a uniform distribution by using the NumPy random.uniform function. The preceding code says, I want a uniformly distributed random set of values that ranges between -10 and 10, and I want 100000 of them. If I then create a histogram of those values, you can see it looks like the following.

There's pretty much an equal chance of any given value or range of values occurring within that data. So, unlike the normal distribution, where we saw a concentration of values near the mean, a uniform distribution has equal probability across any given value within the range that you define.

So what would the probability distribution function of this look like? Well, I'd expect to see basically nothing outside of the range of -10 or beyond 10. But when I'm between -10 and 10, I would see a flat line because there's a constant probability of any one of those ranges of values occurring. So in a uniform distribution you would see a flat line on the probability distribution function because there is basically a constant probability. Every value, every range of values has an equal chance of appearing as any other value.