R: Gauss-Hermite Quadrature Approximation to Expectation for...

gauss.hermite {spatstat.random} | R Documentation

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

### Description

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

### 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 R language 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.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

, Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk.

### Examples

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

[Package spatstat.random version 2.1-0 Index]