unitBall_normGauss-class {multIntTestFunc}

An S4 class to represent the function \frac{1}{(2\pi)^{n/2}}\exp(-\Vert\vec{x}\Vert_2^2/2) on B^{n}

Description

Implementation of the function

f \colon B_n \to [0,\infty),\, \vec{x} \mapsto f(\vec{x}) = \frac{1}{(2\pi)^{n/2}}\exp(-\Vert\vec{x}\Vert_2^2/2) = \frac{1}{(2\pi)^{n/2}}\exp(-\frac{1}{2}\sum_{i=1}^n x_i^2),

where n \in \{1,2,3,\ldots\} is the dimension of the integration domain B_n = \{\vec{x}\in R^n : \Vert \vec{x} \Vert_2 \leq 1\}. In this case the integral is know to be

\int_{B_n} f(\vec{x}) d\vec{x} = P[Z \leq 1] = F_{\chi^2_n}(1),

where Z follows a chisquare distribution with n degrees of freedom.

Details

The instance needs to be created with one parameter representing n.

Slots

dim

An integer that captures the dimension

Author(s)

Klaus Herrmann

Examples

n <- as.integer(3)
f <- new("unitBall_normGauss",dim=n)