# randomgen.mtrand.RandomState.vonmises¶

- RandomState.vonmises(
*mu*,*kappa*,*size=None*)¶ Draw samples from a von Mises distribution.

Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (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 floatsMode (“center”) of the distribution.

**kappa**float or array_like of floatsDispersion of the distribution, has to be >=0.

**size**int or tuple of ints, optionalOutput 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 scalarDrawn samples from the parameterized von Mises distribution.

See also

`scipy.stats.vonmises`

probability density function, distribution, or cumulative density function, etc.

Notes

The probability density for the von Mises distribution is

\[p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)},\]where \(\mu\) is the mode and \(\kappa\) the dispersion, and \(I_0(\kappa)\) 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.

References

- 1
Abramowitz, M. and Stegun, I. A. (Eds.). “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing,” New York: Dover, 1972.

- 2
von Mises, R., “Mathematical Theory of Probability and Statistics”, New York: Academic Press, 1964.

Examples

Draw samples from the distribution:

>>> mu, kappa = 0.0, 4.0 # mean and dispersion >>> s = np.random.vonmises(mu, kappa, 1000)

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

>>> import matplotlib.pyplot as plt >>> from scipy.special import i0 >>> plt.hist(s, 50, density=True) >>> x = np.linspace(-np.pi, np.pi, num=51) >>> y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa)) >>> plt.plot(x, y, linewidth=2, color='r') >>> plt.show()