spatstat.core (version 2.0-0)

gauss.hermite: 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.

Value

Numeric value, vector or matrix.

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.

Examples

# NOT RUN {
  gauss.hermite(function(x) x^2, 3, 1)
# }