brainpy.math.random.vonmises#
- brainpy.math.random.vonmises(mu, kappa, size=None, key=None)[source]#
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 or array_like of floats) – Mode (“center”) of the distribution.
kappa (float or array_like of floats) – 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)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifmu
andkappa
are both scalars. Otherwise,np.broadcast(mu, kappa).size
samples are drawn.
- Returns:
out – Drawn samples from the parameterized von Mises distribution.
- Return type:
ndarray or scalar
See also
scipy.stats.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
Examples
Draw samples from the distribution:
>>> mu, kappa = 0.0, 4.0 # mean and dispersion >>> s = bm.random.vonmises(mu, kappa, 1000)
Display the histogram of the samples, along with the probability density function:
>>> import matplotlib.pyplot as plt >>> from scipy.special import i0 >>> plt.hist(s, 50, density=True) >>> x = np.linspace(-np.pi, np.pi, num=51) >>> y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa)) >>> plt.plot(x, y, linewidth=2, color='r') >>> plt.show()