# 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, 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 ```
```m <- colMeans( as.matrix( iris[,1:3] ) )