Contour plot (on the sphere) of some spherical rotationally symmetric distributions {Directional}

Contour plot (on the sphere) of some spherical rotationally symmetric distributions

Description

The contour plot (on the sphere) of some spherical rotationally symmetric distributions is produced.

Usage

spher.vmf.contour(mu, k, bgcol = "snow", dat = NULL, col = NULL,
lat = 50, long = 50)
spher.purka.contour(theta, a, bgcol = "snow", dat = NULL, col = NULL,
lat = 50, long = 50)
spher.spcauchy.contour(mu, rho, bgcol = "snow", dat = NULL, col = NULL,
lat = 50, long = 50)
spher.pkbd.contour(mu, rho, bgcol = "snow", dat = NULL, col = NULL,
lat = 50, long = 50)

Arguments

mu

The mean or the median direction, depending on the distribution, a unit vector.

theta

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

k

The concentration parameter (\kappa) of the von Mises-Fisher distribution.

a

The concentration parameter (\alpha) of the Purkayastha distribution.

rho

The concentration parameter (\rho) of the spherical Cauchy distribution.

bgcol

The color of the surface of the sphere.

dat

If you have you want to plot supply them here. This has to be a numerical matrix with three columns, i.e. unit vectors.

col

If you supplied data then choose the color of the points. If you did not choose a color, the points will appear in red.

lat

A positive number determing the range of degrees to move left and right from the latitude center. See the example to better understand this argument.

long

A positive number determing the range of degrees to move up and down from the longitude center. See the example to better understand this argument.

Details

The goal of this function is for the user to see how the von Mises-Fisher, the Purkayastha, the spherical Cauchy or the Poisson kernel based distribution looks like.

Value

A plot containing the contours of the distribution.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

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

Sra S. (2012). A short note on parameter approximation for von Mises-Fisher distributions: and a fast implementation of I_s(x). Computational Statistics, 27(1): 177–190.

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. (2020). Some properties of a Cauchy family on the sphere derived from the Mobius transformations. Bernoulli, 26(4): 3224–3248. https://arxiv.org/pdf/1510.07679.pdf

Golzy M. and Markatou M. (2020). Poisson kernel-based clustering on the sphere: convergence properties, identifiability, and a method of sampling. Journal of Computational and Graphical Statistics, 29(4): 758–770.

Sablica L., Hornik K. and Leydold J. (2023). Efficient sampling from the PKBD distribution. Electronic Journal of Statistics, 17(2): 2180–2209.

See Also

spher.esag.contour, spher.mixvmf.contour, kent.contour

Examples

mu <- colMeans( as.matrix( iris[, 1:3] ) )
mu <- mu / sqrt( sum(mu^2) )
## the lat and long are decreased to 30. Increase them back to 50 to
## see the difference
spher.spcauchy.contour(mu, 0.7, lat = 30, long = 30)