Directional (version 5.7)

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

dkent(y, G, param, logden = FALSE )
desag(y, mu, gam, logden = FALSE)

Value

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

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.

mu

The mean vector the ESAG distribution, a vector in \(R^3\).

gam

The two gamma parameters of the ESAG distribution.

logden

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

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

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, esag.mle

Examples

m <- colMeans( as.matrix( iris[,1:3] ) )
y <- rkent(1000, k = 10, m = m, b = 4)
mod <- kent.mle(y)
dkent( y, G = mod$G, param = mod$param )