vMF (version 0.0.4)

dvMF: 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)

Value

the densities computed at each point

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.

Author

Aristide Houndetoungan <>

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.

References

Wood, A. T. (1994). Simulation of the von Mises Fisher distribution. Communications in statistics-simulation and computation, 23(1), 157-164. tools:::Rd_expr_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. tools:::Rd_expr_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))