CpvMF {vMF}

Normalization constant of von Mises - Fisher distribution.

Description

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

Usage

CpvMF(p, k)

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.

Value

the normalization constant.

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 dvMF

Examples

CpvMF(2,3.1)