vonmises(self, mu, kappa, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.vonmises.
Some inconsistencies with the Dask version may exist.
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.
New code should use the vonmises
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
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.
Mode ("center") of the distribution.
Dispersion of the distribution, has to be >=0.
Output 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.
Drawn samples from the parameterized von Mises distribution.
Draw samples from a von Mises distribution.
Generator.vonmises
which should be used for new code.
scipy.stats.vonmises
probability density function, distribution, or cumulative density function, etc.
Draw samples from the distribution:
This example is valid syntax, but we were not able to check execution>>> mu, kappa = 0.0, 4.0 # mean and dispersion # doctest: +SKIP
... s = np.random.vonmises(mu, kappa, 1000) # doctest: +SKIP
Display the histogram of the samples, along with the probability density function:
This example is valid syntax, but we were not able to check execution>>> import matplotlib.pyplot as plt # doctest: +SKIPSee :
... from scipy.special import i0 # doctest: +SKIP
... plt.hist(s, 50, density=True) # doctest: +SKIP
... x = np.linspace(-np.pi, np.pi, num=51) # doctest: +SKIP
... y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa)) # doctest: +SKIP
... plt.plot(x, y, linewidth=2, color='r') # doctest: +SKIP
... plt.show() # doctest: +SKIP
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