Univariate Gauss-Hermite quadrature rule

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Description

Create a univariate Gauss-Hermite quadrature rule.

Usage

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  GHrule(ord, asMatrix = TRUE)

Arguments

ord

scalar integer between 1 and 25 - the order, or number of nodes and weights, in the rule. When the function being multiplied by the standard normal density is a polynomial of order 2k-1 the rule of order k integrates the product exactly.

asMatrix

logical scalar - should the result be returned as a matrix. If FALSE a data frame is returned. Defaults to TRUE.

Details

This version of Gauss-Hermite quadrature provides the node positions and weights for a scalar integral of a function multiplied by the standard normal density.

Originally based on package SparseGrid's hidden GQN().

Value

a matrix (or data frame, is asMatrix is false) with ord rows and three columns which are z the node positions, w the weights and ldnorm, the logarithm of the normal density evaluated at the nodes.

See Also

a different interface is available via GQdk().

Examples

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(r5 <- GHrule(5, asMatrix=FALSE))
## second, fourth, sixth, eighth and tenth central moments of the
## standard Gaussian density
with(r5, sapply(seq(2, 10, 2), function(p) sum(w * z^p)))

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