fastGHQuad-package {fastGHQuad}

A package for fast, numerically-stable computation of Gauss-Hermite quadrature rules

Description

This package provides functions to compute Gauss-Hermite quadrature rules very quickly with a higher degree of numerical stability (tested up to 2000 nodes).

Details

It also provides function for adaptive Gauss-Hermite quadrature, extending Laplace approximations (as in Liu & Pierce 1994).

Package:	fastGHQuad
Type:	Package
License:	MIT
LazyLoad:	yes

Author(s)

Alexander W Blocker

Maintainer: Alexander W Blocker <[e-mail]>

References

Golub, G. H. and Welsch, J. H. (1969). Calculation of Gauss Quadrature Rules. Mathematics of Computation 23 (106): 221-230.

Liu, Q. and Pierce, D. A. (1994). A Note on Gauss-Hermite Quadrature. Biometrika, 81(3) 624-629.

See Also

gaussHermiteData, aghQuad, ghQuad

Examples

# Get quadrature rule
rule <- gaussHermiteData(1000)

# Find a normalizing constant
g <- function(x) 1/(1+x^2/10)^(11/2) # t distribution with 10 df
aghQuad(g, 0, 1.1, rule)
# actual is
1/dt(0,10)

# Find an expectation
g <- function(x) x^2*dt(x,10) # t distribution with 10 df
aghQuad(g, 0, 1.1, rule)
# actual is 1.25