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
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where
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is the mode and
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the dispersion,
and
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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)