A package for fast, numerically-stable computation of Gauss-Hermite quadrature rules
This package provides functions to compute Gauss-Hermite quadrature rules very quickly with a higher degree of numerical stability (tested up to 2000 nodes). package
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 |
# 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
Alexander W Blocker
Maintainer: Alexander W Blocker ablocker@gmail.com
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.
gaussHermiteData, aghQuad, ghQuad