# dvmf: Density of some (hyper-)spherical distributions In Directional: A Collection of Functions for Directional Data Analysis

 Density of some (hyper-)spherical distributions R Documentation

## 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.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

### 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.

kent.mle, rkent, esag.mle 
m <- colMeans( as.matrix( iris[,1:3] ) )