`numpy.random._generator:Generator.vonmises`

Signature

def vonmises ( mu , kappa , size = None )

Summary

Draw samples from a von Mises distribution.

Extended Summary

Samples are drawn from a von Mises distribution with specified mode (mu) and concentration (kappa), on the interval [-pi, pi].

The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution.

Parameters

mu : float or array_like of floats: Mode ("center") of the distribution.
kappa : float or array_like of floats: Concentration of the distribution, has to be >=0.
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if mu and kappa are both scalars. Otherwise, np.broadcast(mu, kappa).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized von Mises distribution.

Notes

The probability density for the von Mises distribution is

p (x) = \frac{e ^{κ cos (x - μ)}}{2 π I _{0} ( κ )},

where $μ$ is the mode and $κ$ the concentration, and $I_{0} (κ)$ is the modified Bessel function of order 0.

The von Mises is named for Richard Edler von Mises, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science.

Examples

Draw samples from the distribution:

mu, kappa = 0.0, 4.0 # mean and concentration
rng = np.random.default_rng()
s = rng.vonmises(mu, kappa, 1000)

✓

Display the histogram of the samples, along with the probability density function:

import matplotlib.pyplot as plt

✓

plt.hist(s, 50, density=True)

✗

x = np.linspace(-np.pi, np.pi, num=51)
plt.show()

✓

Aliases

numpy.random.Generator.vonmises