Uniform Distribution

Uniform-Distributionsize5000.png
Uniform-Distributionsize5000

Uniform Distribution or Rectangular Distribution

Uniform distribution or rectangular distribution is a continuous probability distribution.
Definition-
A random variable X is said to follow uniform or rectangular distribution it follows the following probability distribution function.

And is denoted by X~U(a,b)

Uniform Distribution PDF


Python Code to Plot Uniform Distribution

import numpy
import matplotlib.pyplot as plt
a=20
b=50
x= numpy.random.uniform(low=a,high=b,size=100)
plt.title(“Uniform Distribution(size=100)”)
plt.plot(x)
plt.savefig(“Uniform Distribution(size=100).png”)


Uniform Distribution(size=100)

                                                          Uniform Distribution(size=100)


Uniform Distribution(size=1000)

Uniform Distribution(size=1000)


https://cdn.shortpixel.ai/client/q_lossy,ret_img,w_640/https://www.postnetwork.co/wp-content/uploads/Uniform-Distributionsize2000.png


And when size=5000 it becomes almost rectangular

Uniform-Distributionsize5000.png

Uniform-Distributionsize5000

 

Mean for Uniform Distribution

Mean-Uniform Distribution

Variance  for Uniform  Distribution

Applications of Uniform Distribution-

Uniform distribution is widely used by simulators.

  • Monte Carlo simulator uses it in risk analysis.
  • Network simulators use to set   traffic generation parameters.

Conclusion-

Uniform probability distribution is a simple continuous probability distribution.  Further, it helps to understand basics of probability distribution.  If you want to learn probability distribution functions  in statistics start from uniform distribution.

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