Directional (version 6.8)

Density of the spherical ESAG and Kent distributions and of the ESAG distribution in arbitrary dimensions: Density of the spherical ESAG and Kent distributions

Description

Density of the spherical ESAG and Kent distributions.

Usage

desag(y, mu, gam, logden = FALSE)
dkent(y, G, param, logden = FALSE)
dESAGd(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. For the dESAGd it can have any dimension.

mu

The mean vector the ESAG distribution.

gam

The two \(\gamma\) parameters of the ESAG distribution.

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.

logden

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

Author

Michail Tsagris and Zehao Yu.

R implementation and documentation: Michail Tsagris and Zehao Yu .

Details

The density of the spherical ESAG or Kent distribution, or of the ESAG distribution in arbitrary dimensions is computed.

References

Zehao Yu and Xianzheng Huang (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension. Electronic Journal of Statististics, 18(1): 301--334.

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.

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

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

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 )