dvmf: Density of some (hyper-)spherical distributions

In Directional: A Collection of Functions for Directional Data Analysis

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)
dpkbd(y, mu, rho, logden = FALSE)

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, the spherical Cauchy distribution, or of the Poisson kernel-based 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, or of the Poisson kernel-based distribution.
logden	If you the logarithm of the density values set this to TRUE.

Details

The density of the von Mises-Fisher, of the IAG, of the Purkayastha, of the spherical Cauchy distribution, or of the Poisson kernel-based distribution is computed.

Value

A vector with the (log) density values of y.

Author(s)

Michail Tsagris and Zehao Yu.

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

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. (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.

Zehao Yu and Xianzheng Huang (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension. Electronic Journal of Statististics, 18(1): 301–334.

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

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)

Directional documentation built on Oct. 30, 2024, 9:15 a.m.