Univariate Gauss-Hermite quadrature rule
Create a univariate Gauss-Hermite quadrature rule.
GHrule(ord, asMatrix = TRUE)
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 |
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().
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.
a different interface is available via GQdk().
(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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