fb.saddle: Saddlepoint approximations of the Fisher-Bingham...

View source: R/fb.saddle.R

Saddlepoint approximations of the Fisher-Bingham distributionsR Documentation

Saddlepoint approximations of the Fisher-Bingham distributions


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


fb.saddle(gam, lam)



A numeric vector containing the parameters of the Fisher part.


All the eigenvalues of the Bingham part. Not just the non zero ones.


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


A list including:

first oder

The first order approximation

second oder

The second order approximation

third oder

The third order approximation


Michail Tsagris.

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


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


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)

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