Python random.vonmisesvariate() Method

Therandom.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 asmu andkappa define the distribution's characteristics, wheremu is the mean angle expressed in radians, which should be between 0 and 2, andkappa, 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

Thisrandom.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 therandom.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 randomimport math# mean angle in radiansmu = math.pi  # concentration parameterkappa = 1  # Generate a von Mises distributed random numberrandom_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 therandom.vonmisesvariate() method.

import random# mean angle in radiansmu = 0# concentration parameter kappa = 3# list to store generated wave directionsresult = []# Generate a list of random numbers from the von Mises distributionfor _ 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 therandom.vonmisesvariate() method.

import randomimport mathimport matplotlib.pyplot as plt# mean angle in radiansmu = 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 plotsfig = plt.figure(figsize=(7, 4))# Plotting for each set of parametersplot_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 titleplt.title('von Mises Distributions with Different Concentration Parameters')plt.legend()# Show plotplt.show()

The output of the above code is as follows −