von Mises distribution

The parameters kappa and mu match those used in the wikipedia article:

https://en.wikipedia.org/wiki/Von_Mises_distribution

mpsci.distributions.vonmises.circmean(kappa, mu=0)

Circular mean of the von Mises distribution.

The circular mean of the distribution is mu.

mpsci.distributions.vonmises.circvar(kappa, mu=0)

Circular variance of the von Mises distribution.

This is

1 - I1(kappa)/I0(kappa)

where I0 and I1 are the modified Bessel functions of the first kind.

mpsci.distributions.vonmises.entropy(kappa, mu=0)

Differential entropy of the von Mises distribution.

mpsci.distributions.vonmises.logpdf(x, kappa, mu=0)

Natural logarithm of the PDF of the von Mises distribution.

mpsci.distributions.vonmises.pdf(x, kappa, mu=0)

Probability density function of the von Mises distribution.

mpsci.distributions.vonmises.support(kappa, mu=0)

Support of the von Mises distribution.

The von Mises distribution is periodic, so the PDF is nonzero at any x value. However, the most useful definition of support for this distribution is the fundamental period of the distribution. So this function returns (-pi + mu, pi + mu). Then, for example, the integral of the PDF over the support results in the expected value of 1.