Directional (version 3.4)

Density of the spherical Kent distribution: Density of the spherical Kent distribution

Description

Density of the spherical Kent distribution.

Usage

kent.density(y, G, param, 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.

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 ESAG distribution, on the sphere, 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 = 5)
mod <- kent.mle(y)
kent.density( y, G = mod$G, param = mod$param )
# }