| 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 |
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 rolfturner@posteo.net
and Ege Rubak rubak@math.aau.dk.
Examples
gauss.hermite(function(x) x^2, 3, 1)