# GHrule

##### Univariate Gauss-Hermite quadrature rule

Create a univariate Gauss-Hermite quadrature rule.

##### Usage

`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

```
# NOT RUN {
(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)))
# }
```

*Documentation reproduced from package lme4, version 1.1-21, License: GPL (>= 2)*