Python random.vonmisesvariate() Method

The random.vonmisesvariate() method in Python generates random numbers that follows the von Mises distribution, also known as the circular normal distribution or Tikhonov distribution. This distribution is used in probability theory and directional statistics to model data on a circular domain, such as angles. Parameters such as mu and kappa define the distribution's characteristics, where mu is the mean angle expressed in radians, which should be between 0 and 2, and kappa, the concentration parameter, must be greater than or equal to zero.

Note − This function is not accessible directly, so we need to import the random module and then we need to call this function using random static object.

Syntax

Following is the syntax of vonmisesvariate() method −

random.vonmisesvariate(mu, kappa)

Parameters

The Python random.vonmisesvariate() method takes two parameters −

• mu: This is the mean angle, expressed in radians, which should be between 0 and 2.

1

• sigma: This is the concentration parameter, which must be greater than or equal to zero. It measures how concentrated the distribution is around the mean angle. When kappa is zero, the distribution becomes uniform over the range 0 to 2.

Return Value

This random.vonmisesvariate() method returns a random number that follows the von Mises distribution (circular normal distribution).

Example 1

Let's see a basic example of using the random.vonmisesvariate() method for generating a random number from a von Mises distribution with a mean angle of (180 degrees) and a concentration parameter of 1.

import random
import math

# mean angle in radians
mu = math.pi  

# concentration parameter
kappa = 1  

# Generate a von Mises distributed random number
random_angle = random.vonmisesvariate(mu, kappa)

print('A random number from von Mises distribution:',random_angle)

Following is the output −

A random number from von Mises distribution: 1.5637865003055311

Note: The Output generated will vary each time you run the program due to its random nature.

Example 2

This example generates a list of 10 random numbers that follows the von Mises distribution using the random.vonmisesvariate() method.

import random

# mean angle in radians
mu = 0

# concentration parameter 
kappa = 3

# list to store generated wave directions
result = []

# Generate a list of random numbers from the von Mises distribution
for _ in range(10):
    direction = random.vonmisesvariate(mu, kappa)
    result.append(direction)

print("List of random numbers from von Mises distribution:", result)

While executing the above code you will get the similar output like below −

List of random numbers from von Mises distribution: [5.888313245257218, 0.12280876945454619, 0.3877094476451274, 5.807284393939756, 0.4416696367838093, 6.165324081139434, 5.783168359038133, 6.05815219609358, 5.889178104771408, 5.946514998727608]

Example 3

Here is another example that generates and visualizes von Mises distributions with different concentration parameters (kappa) using the random.vonmisesvariate() method.

import random
import math
import matplotlib.pyplot as plt

# mean angle in radians
mu = math.pi / 2  

def plot_vonmises(mu, kappa, label, color):

    # Generate von Mises-distributed data
    data = [random.vonmisesvariate(mu, kappa) for _ in range(10000)]

    # Plot histogram of the generated data
    plt.hist(data, bins=100, density=True, alpha=0.5, color=color, label=r'(mu=$\pi/2$, k={})'.format(kappa))

# Create a figure for the plots
fig = plt.figure(figsize=(7, 4))

# Plotting for each set of parameters
plot_vonmises(mu, 0, '0, 0', 'blue')
plot_vonmises(mu, 0.5, '0, 0.5', 'green')
plot_vonmises(mu, 1, '0, 1', 'yellow')
plot_vonmises(mu, 2, '0, 2', 'red')
plot_vonmises(mu, 8, '0, 8', 'pink')

# Adding labels and title
plt.title('von Mises Distributions with Different Concentration Parameters')
plt.legend()

# Show plot
plt.show()

The output of the above code is as follows −