Directional (version 4.0)

Density of some (hyper-)spherical distributions: Density of some (hyper-)spherical distributions

Description

Density of some (hyper-)spherical distributions.

Usage

vmf.density(y, k, mu, logden = FALSE )
iag.density(y, mu, logden = FALSE)
purka.density(y, a, theta, logden = FALSE)

Arguments

y

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

k

The concentration parameter of the von Mises-Fisher distribution.

a

The concentration parameter of the Purkayastha distribution.

mu

The mean direction (unit vector) of the von Mises-Fisher distribution or the mean direction of the IAG distribution.

theta

The median direction for the Purkayastha distribution.

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 von Mises-Fisher, of the IAG or of the Purkayastha 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.

Purkayastha S. (1991). A Rotationally Symmetric Directional Distribution: Obtained through Maximum Likelihood Characterization. The Indian Journal of Statistics, Series A, 53(1): 70-83

Cabrera J. and Watson G. S. (1990). On a spherical median related distribution. Communications in Statistics-Theory and Methods, 19(6): 1973-1986.

See Also

kent.mle, rkent, ESAGmle

Examples

# NOT RUN {
m <- colMeans( as.matrix( iris[,1:3] ) )
y <- rvmf(1000, m = m, k = 10)
vmf.density(y, k=10, m )
# }