Directional (version 6.1)

Contour plots of some rotational symmetric distributions: Contour plots of some rotational symmetric distributions

Description

Contour plots of some rotational symmetric distributions.

Usage

vmf.contour(k)
spcauchy.contour(mu, rho, lat = 50, long = 50)
purka.contour(theta, a, 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 or the spherical Cauchy distribution.

rho

The \(\rho\) parameter of the spherical Cauchy 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

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

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.

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

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)
# }