bdvmf {Ball} | R Documentation |
Simulated von Mises-Fisher Data
Description
Simulated random vectors following the von Mises-Fisher distribution
with mean direction \mu_{x}=(1, 0, 0)
and \mu_{y}=(1, 1, 1)
,
and concentration parameter is \kappa = 3
.
Format
bdvmf$x
: A 300 \times 3
numeric matrix containing simulated von Mises-Fisher data.
bdvmf$group
: A group index vector.
Details
In directional statistics, the von Mises–Fisher distribution
(named after Ronald Fisher and Richard von Mises), is a probability distribution
on the (p-1)
-dimensional sphere in R^{p}
The parameters \mu
, and \kappa
, are called the mean direction and concentration
parameter, respectively. The greater the value of \kappa
,
the higher the concentration of the distribution around the mean
direction \mu
,. The distribution is unimodal for \kappa
,
and is uniform on the sphere for \kappa=0
.
References
Embleton, N. I. Fisher, T. Lewis, B. J. J. (1993). Statistical analysis of spherical data (1st pbk. ed.). Cambridge: Cambridge University Press. pp. 115–116. ISBN 0-521-45699-1.