# unitBall_normGauss-class: An S4 class to represent the function... In multIntTestFunc: Provides Test Functions for Multivariate Integration

## Description

Implementation of the function

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

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

\int_{B_n} f(\vec{x}) d\vec{x} = P[Z ≤q 1] = F_{χ^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

## Examples

 1 2 n <- as.integer(3) f <- new("unitBall_normGauss",dim=n) 

multIntTestFunc documentation built on Oct. 5, 2021, 5:08 p.m.