Directional (version 7.0)

Saddlepoint approximations of the Fisher-Bingham distributions: 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)

Value

A list including:

first oder

The first order approximation

second oder

The second order approximation

third oder

The third order approximation

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.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris and Giorgos Athineou <[e-mail]>.

Details

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

References

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

See Also

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
fb.saddle( c(0, k, 0), c(0, 0, 0) ) ## saddlepoint approximation

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