| dvMF {vMF} | R Documentation |
PDF of the von Mises - Fisher distribution.
Description
dvMF computes the density of the von Mises - Fisher distribution, given a set of spherical coordinates and the distribution parameters.
Usage
dvMF(z, theta)
Arguments
z |
as the set of points at which the spherical coordinate will be evaluated. z may be an one row matrix or vector if it contain one spherical coordinates or a matrix whose each row is one spherical coordinates. |
theta |
as the distribution parameter. |
Details
The probability density function of the von Mises - Fisher distribution is defined by :
f(z|theta) = C_p(|theta|)\exp{(z theta)}
|theta| is the intensity parameter and \frac{theta}{|theta|} the mean directional parameter. The normalization constant C_p() depends
on the Bessel function of the first kind. See more details here.
Value
the densities computed at each point
Author(s)
Aristide Houndetoungan <ariel92and@gmail.com>
References
Wood, A. T. (1994). Simulation of the von Mises Fisher distribution. Communications in statistics-simulation and computation, 23(1), 157-164. doi:10.1080/03610919408813161.
Hornik, K., & Grun, B. (2014). movMF: An R package for fitting mixtures of von Mises-Fisher distributions. Journal of Statistical Software, 58(10), 1-31. doi:10.18637/jss.v058.i10.
See Also
rvMF and CpvMF
Examples
{}
# Draw 1000 vectors from vM-F with parameter 1, (1,0)
z <- rvMF(1000,c(1,0))
# Compute the density at these points
dvMF(z,c(1,0))
# Density of (0,1,0,0) with the parameter 3, (0,1,0,0)
dvMF(c(0,1,0,0),c(0,3,0,0))