numpy.random.vonmises

numpy.random.vonmises(mu=0.0, kappa=1.0, 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 circle. It may be thought of as the circular analogue of the normal distribution.

Parameters:

mu : float

Mode (“center”) of the distribution.

kappa : float, >= 0.

Dispersion of the distribution.

size : {tuple, int}

Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn.

Returns:

samples : {ndarray, scalar}

The returned samples live on the unit circle [-pi, pi].

See also

scipy.stats.distributions.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, named for Richard Edler von Mises, 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

[R125]

Abramowitz, M. and Stegun, I. A. (ed.), Handbook of Mathematical Functions, National Bureau of Standards, 1964; reprinted Dover Publications, 1965.

[R126]

von Mises, Richard, 1964, Mathematical Theory of Probability and Statistics (New York: Academic Press).

[R127]

Wikipedia, “Von Mises distribution”, http://en.wikipedia.org/wiki/Von_Mises_distribution

Examples