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

## Description

Density of some (hyper-)spherical distributions.

## Usage

 ```1 2 3``` ```dvmf(y, k, mu, logden = FALSE ) iagd(y, mu, logden = FALSE) dpurka(y, a, theta, logden = FALSE) ```

## Arguments

 `y` A matrix or a vector with the data expressed in Euclidean coordinates, i.e. unit vectors. `k` The concentration parameter of the von Mises-Fisher distribution. `a` The concentration parameter of the Purkayastha distribution. `mu` The mean direction (unit vector) of the von Mises-Fisher distribution or the mean direction of the IAG distribution. `theta` The median direction for the Purkayastha 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 or of the Purkayastha 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.

Kent John (1982). The Fisher-Bingham distribution on the sphere. Journal of the Royal Statistical Society, Series B, 44(1): 71-80.

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.

```kent.mle, rkent, esag.mle ```
 ```1 2 3``` ```m <- colMeans( as.matrix( iris[,1:3] ) ) y <- rvmf(1000, m = m, k = 10) dvmf(y, k=10, m ) ```