# gauss.hermite

##### Gauss-Hermite Quadrature Approximation to Expectation for Normal Distribution

Calculates an approximation to the expected value of any function of a normally-distributed random variable, using Gauss-Hermite quadrature.

- Keywords
- math

##### Usage

`gauss.hermite(f, mu = 0, sd = 1, ..., order = 5)`

##### Arguments

- f
- The function whose moment should be approximated.
- mu
- Mean of the normal distribution.
- sd
- Standard deviation of the normal distribution.
- ...
- Additional arguments passed to
`f`

. - order
- Number of quadrature points in the Gauss-Hermite quadrature approximation. A small positive integer.

##### Details

This algorithm calculates the approximate expected value of
`f(Z)`

when `Z`

is a normally-distributed random
variable with mean `mu`

and standard deviation `sd`

.
The expected value is an integral with respect to the
Gaussian density; this integral is approximated
using Gauss-Hermite quadrature.

The argument `f`

should be a function in the Rlanguage
whose first argument is the variable `Z`

. Additional arguments
may be passed through `...`

. The value returned by `f`

may be a single numeric value, a vector, or a matrix. The values
returned by `f`

for different values of `Z`

must have
compatible dimensions.

The result is a weighted average of several values of `f`

.

##### Value

- Numeric value, vector or matrix.

##### Examples

`gauss.hermite(function(x) x^2, 3, 1)`

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*