# fb.saddle: Saddlepoint approximations of the Fisher-Bingham... In Directional: A Collection of Functions for Directional Data Analysis

 Saddlepoint approximations of the Fisher-Bingham distributions R Documentation

## Saddlepoint approximations of the Fisher-Bingham distributions

### Description

It calculates the logarithm of the normalising constant of the Fisher-Bingham distribution.

### Usage

``````fb.saddle(gam, lam)
``````

### Arguments

 `gam` A numeric vector containing the parameters of the Fisher part. `lam` All the eigenvalues of the Bingham part. Not just the non zero ones.

### Details

It calculate the three approximations given by Kume and Wood (2005) and it uses the Fisher-Bingham parametrization of that paper.

### Value

A list including:

 `first oder` The first order approximation `second oder` The second order approximation `third oder` The third order approximation

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.

### References

Kume Alfred and Wood Andrew T.A. (2005). Saddlepoint approximations for the Bingham and Fisher-Bingham normalizing constants. Biometrika, 92(2):465-476

```kent.logcon, rfb, kent.mle, rbingham ```

### Examples

``````p <- 3  ;  k <- 1
0.5 * p * log(2 * pi) - (p/2 - 1) * log(k) + log( besselI(k, p/2 - 1, expon.scaled = TRUE) ) + k
## normalising constant of the
## von Mises-Fisher distribution

## Normalising constant of the Kent distribution
fb.saddle( c(0, 10, 0), c(0, -2, 2) )
kent.logcon(10, 2)
``````

Directional documentation built on Oct. 12, 2023, 1:07 a.m.