Saddlepoint approximations of the Fisher-Bingham distributions
It calculates the logarithm of the normalising constant of the Fisher-Bingham distribution.
fb.saddle(gam, lam)
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. |
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
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)
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