Saddlepoint approximations of the Fisher-Bingham distributions

Description

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

Usage

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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@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>

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

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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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