Directional (version 3.7)

Density of the von Mises-Fisher and the spherical Kent distributions: Density of the spherical Kent distribution

Description

Density of the spherical Kent distribution.

Usage

kent.density(y, G, param, logden = FALSE )
vmf.density(y, k, mu, logden = FALSE)

Arguments

y

A matrix or a vector with the data expressed in Euclidean coordinates, i.e. unit vectors.

G

A 3 x 3 matrix whose first column is the mean direction. The second and third columns are the major and minor axes respectively.

param

A vector with the concentration \(\kappa\) and ovalness \(\beta\) parameters. The \(\psi\) has been absorbed inside the matrix G.

k

The concentration parameter of the von Mises-Fisher distribution.

mu

The mean direction of the von Mises-Fisher distribution.

logden

If you the logarithm of the density values set this to TRUE.

Value

A vector with the density values of y.

Details

The density of the von Mises-Fisher or of the spherical Kent distribution is computed.

References

Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

Kent John (1982). The Fisher-Bingham distribution on the sphere. Journal of the Royal Statistical Society, Series B, 44(1): 71-80.

See Also

kent.mle, rkent, ESAGmle

Examples

# NOT RUN {
m <- colMeans( as.matrix( iris[,1:3] ) )
y <- rkent(1000, k = 10, m = m, b = 4)
mod <- kent.mle(y)
kent.density( y, G = mod$G, param = mod$param )
# }