numpy.random.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
Mode (“center”) of the distribution.
kappa : float
Dispersion 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. Default is None, in which case a single value is returned.
Returns: samples : scalar or ndarray
The returned samples, which are in the interval [-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 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
Abramowitz, M. and Stegun, I. A. (ed.), Handbook of Mathematical Functions, New York: Dover, 1965.
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 >>> import scipy.special as sps >>> count, bins, ignored = plt.hist(s, 50, normed=True) >>> x = np.arange(-np.pi, np.pi, 2*np.pi/50.) >>> y = -np.exp(kappa*np.cos(x-mu))/(2*np.pi*sps.jn(0,kappa)) >>> plt.plot(x, y/max(y), linewidth=2, color='r') >>> plt.show()
(Source code, png, pdf)