Directional (version 7.0)

Contour plots of some rotationally symmetric distributions: Contour plots of some rotationally symmetric distributions

Description

Contour plots of some rotationally symmetric distributions.

Usage

vmf.contour(k)
spcauchy.contour(mu, rho, lat = 50, long = 50)
purka.contour(theta, a, lat = 50, long = 50)
pkbd.contour(mu, rho, lat = 50, long = 50)

Value

A contour plot of the distribution.

Arguments

k

The concentration parameter.

mu

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

rho

The \(\rho\) parameter of the spherical Cauchy distribution, or the Poisson kernel-based distribution.

theta

The median direction for the Purkayastha distribution, a unit vector.

a

The concentration parameter of the Purkayastha distribution.

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.

Author

Michail Tsagris and Christos Adam.

R implementation and documentation: Michail Tsagris and Christos Adam .

Details

The user specifies the concentration parameter only and not the mean direction or data. This is for illustration purposes only. The graph of the von Mises-Fisher distribution will always contain circles, as this distribution is the analogue of a bivariate normal in two dimensions with a zero covariance.

References

Tsagris M., Papastamoulis P. and Kato S. (2024). Directional data analysis using the spherical Cauchy and the Poisson kernel-based distribution. https://arxiv.org/pdf/2409.03292.

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

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

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.

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

rvmf, vmf.mle, vmf.kerncontour, kent.contour, sphereplot

Examples

# \donttest{
vmf.contour(5)
mu <- colMeans( as.matrix( iris[,1:3] ) )
mu <- mu / sqrt( sum(mu^2) )
spcauchy.contour(mu, 0.7, 30, 30)
spcauchy.contour(mu, 0.7, 60, 60)
# }