hgm (version 1.10)

hgm.ncBingham: The function hgm.ncBingham performs the holonomic gradient method (HGM) for Bingham distributions.

Description

The function hgm.ncBingham performs the holonomic gradient method (HGM) for Bingham distributions with the deSolve package in R.

Usage

hgm.ncBingham(th, d=rep(1,length(th)+1), logarithm=FALSE,
               ini.method="power", times=NULL, withvol=FALSE, ...)

Arguments

th

A (p-1)-dimensional vector which specifies the first (p-1) components of the parameter vector of the Bingham distribution on the (p-1)-dim sphere. The p-th parameter is assumed to be zero.

d

A p-dimensional vector which specifies the multiplicity of the parameter. The default is all-one vector.

logarithm

If 'logarithm' is TRUE, then the result is log of the normalizing constant.

ini.method

The method for computing the initial value. Only "power" is implemented now.

times

a vector; times in [0,1] at which explicit estimates for G are desired. If time = NULL, the set {0,1} is used, and only the final value is returned.

withvol

If 'withvol' is TRUE, then the normalizing constant with volume of sphere is returned. Otherwise that without volume is returned. Therefore, if 'withvol' is FALSE and the parameter is zero, then the normalizing constant becomes 1.

...

Additional parameters for computing initial values. Details are omitted.

Value

• The output is p-dimensional vector G. The first element of G is the normalizing constant and the following (p-1)-elements are partial derivative of the normalizing constant with respect to the first (p-1) components of the parameter 'th'.

Details

The function hgm.ncBingham computes the normalizing constant of the Bingham distribution and its derivatives at any specified point. The initial value is computed by the power series expansion.

References

http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/ref-hgm.html

Examples

# Example 1.
hgm.ncBingham(c(1,3,5))