Directional (version 4.0)

Density of the spherical Kent and ESAG distributions: Density of the spherical Kent and ESAG distributions

Description

Density of the spherical Kent and ESAG distributions.

Usage

kent.density(y, G, param, logden = FALSE )
ESAGdensity(y, param, logden = FALSE)

Arguments

y

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

G

For the Kent distribution only, 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

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

For the ESAG distribution, its parameters, the first three are the mean vector in \(R^3\) and the next two are the two gammas.

logden

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

Value

A vector with the (log) density values of y.

Details

The density of the spherical Kent or spherical ESAG 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.

Paine P.J., Preston S.P., Tsagris M. and Wood A.T.A. (2018). An Elliptically Symmetric Angular Gaussian Distribution. Statistics and Computing, 28((3):689--697.

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 )
# }