vMF (version 0.0.4)

CpvMF: Normalization constant of von Mises - Fisher distribution.

Description

CpvMF returns the normalization constant of von Mises - Fisher density.

Usage

CpvMF(p, k)

Value

the normalization constant.

Arguments

p

as sphere dimension.

k

as the intensity 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.

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 dvMF

Examples

CpvMF(2,3.1)