How to model the uniform distribution in Python
Overview
A uniform distribution is a probability distribution where every event has an equal likelihood or chance of happening.
Its probability density function is as shown below:
when is and and if or .
When a value or variable follows a uniform distribution, the probability of an event occurring is shown by
, where N is the number of events likely to occur.
Practical applications of the uniform distribution
Uniform distribution is applicable where the likelihood of an event occurring is the same all through, such as when you roll a die one time, the probability that it falls on a number between 1 and 6 follows a uniform distribution because each number is equally likely to occur.
For example, there are 6 possible numbers the die can land on, so the probability that you roll a 1 is 1/6, the probability that you roll a 2 is 1/6, and so on.
Code implementation in Python
There are 2 ways to model a uniform distribution in python.
1. Using the NumPy library in Python.
import numpy as npimport matplotlib.pyplot as pltvalues = np.random.uniform(0.01, 0.99, 1000)count, bins, ignored = plt.hist(values, 20, density=True)plt.plot(bins, np.ones_like(bins),color='r')plt.title('Uniform Distribution')plt.ylabel('Density')plt.xlabel('Values')plt.show()
Explanation
The above code uses NumPy to generate 1,000 random points of a uniform distribution ranging from 0.01 to 0.99 and then visualizes the dataset using a histogram.
The pdf of each point is therefore approximately
2. Using the SciPy library in Python
from scipy.stats import uniformimport matplotlib.pyplot as pltimport numpy as npx = uniform.rvs(0.01,0.99,size=1000)print(f'pdf of x is {uniform.pdf(x[0])}')plt.hist(x,density = True)plt.axhline(y=uniform.pdf(x[0]),color='r')plt.title('Uniform distribution')plt.ylabel('Density')plt.xlabel('X')plt.show()
Explanation
The code above uses Scipy’s uniform method to generate random variables of a uniform distribution and then uses the histogram to display them.
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