Contour plots of some rotationally symmetric distributions {Directional}

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)

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.

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.

Value

A contour plot of the distribution.

Author(s)

Michail Tsagris and Christos Adam.

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

References

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

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)