Introduction to Python Rayleigh Distribution
Python Rayleigh Distribution
The Rayleigh distribution is characterized by a single parameter called the scale parameter (σ)
, which determines the spread or width of the distribution.
The probability density function (PDF) of the Rayleigh distribution is given by:
f(x) = (x / σ^2) * e^(-x^2 / (2 * σ^2))
Where x
is the random variable.
In Python, you can work with the Rayleigh distribution using the numpy.random.rayleigh()
function from the NumPy library. This function allows you to generate random numbers from a Rayleigh distribution.
As an example:
import numpy as np
# Define the scale parameter
scale = 2.5
# Generate random numbers from a Rayleigh distribution
size = 1000
random_numbers = np.random.rayleigh(scale, size=size)
In this example:
np.random.rayleigh(scale, size=size)
generates an array of 1000 random numbers from a Rayleigh distribution with a scale parameter of 2.5.- The resulting array
random_numbers
will contain the generated random numbers.
The Rayleigh distribution is often used to model the amplitude of a random variable when the underlying components have equal variance and are normally distributed. It has applications in signal processing, wireless communication, and reliability analysis.