Directional (version 6.1)

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

Description

Density of some (hyper-)spherical distributions.

Usage

dvmf(y, mu, k, logden = FALSE )
iagd(y, mu, logden = FALSE)
dpurka(y, theta, a, logden = FALSE)
dspcauchy(y, mu, rho, 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.

mu

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

theta

The mean direction (unit vector) of the Purkayastha distribution.

k

The concentration parameter of the von Mises-Fisher distribution.

a

The concentration parameter of the Purkayastha distribution.

rho

The \(\rho\) parameter of the spherical Cauchy 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 von Mises-Fisher, of the IAG, of the Purkayastha or of the spherical Cauchy distribution is computed.

References

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

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.

Kato S. and McCullagh P. (2018). Mobius transformation and a Cauchy family on the sphere. arXiv preprint arXiv:1510.07679.

Kato S. & McCullagh P. (2020). Some properties of a Cauchy family on the sphere derived from the Mobius transformations. Bernoulli, 26(4), 3224--3248.

See Also

kent.mle, rkent, esag.mle

Examples

m <- colMeans( as.matrix( iris[,1:3] ) )
y <- rvmf(1000, m = m, k = 10)
dvmf(y, k=10, m)