# dkent: Density of the spherical Kent and ESAG distributions In Directional: A Collection of Functions for Directional Data Analysis

 Density of the spherical Kent and ESAG distributions R Documentation

## Density of the spherical Kent and ESAG distributions

### Description

Density of the spherical Kent and ESAG distributions.

### Usage

```dkent(y, G, param, logden = FALSE )
desag(y, mu, gam, logden = FALSE)
```

### Arguments

 `y` A matrix or a vector with the data expressed in Euclidean coordinates, i.e. unit vectors. `G` For the Kent distribution only, a 3 x 3 matrix whose first column is the mean direction. The second and third columns are the major and minor axes respectively. `param` For the Kent distribution a vector with the concentration κ and ovalness β parameters. The ψ has been absorbed inside the matrix G. `mu` The mean vector the ESAG distribution, a vector in R^3. `gam` The two gamma parameters of the ESAG distribution. `logden` If you the logarithm of the density values set this to TRUE.

### Details

The density of the spherical Kent or spherical ESAG 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.

Paine P.J., Preston S.P., Tsagris M. and Wood A.T.A. (2018). An Elliptically Symmetric Angular Gaussian Distribution. Statistics and Computing, 28(3):689–697.

```kent.mle, rkent, esag.mle ```

### Examples

```m <- colMeans( as.matrix( iris[,1:3] ) )
y <- rkent(1000, k = 10, m = m, b = 4)
mod <- kent.mle(y)
dkent( y, G = mod\$G, param = mod\$param )
```

Directional documentation built on Sept. 22, 2022, 9:06 a.m.