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
kappa : float, >= 0.
size : {tuple, int}
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Returns : | samples : {ndarray, scalar}
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See also
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
[R246] | Abramowitz, M. and Stegun, I. A. (ed.), Handbook of Mathematical Functions, National Bureau of Standards, 1964; reprinted Dover Publications, 1965. |
[R247] | von Mises, Richard, 1964, Mathematical Theory of Probability and Statistics (New York: Academic Press). |
[R248] | Wikipedia, “Von Mises distribution”, http://en.wikipedia.org/wiki/Von_Mises_distribution |
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()