unitBall_normGauss-class {multIntTestFunc} | R Documentation |
An S4 class to represent the function (2π)n/21exp(−∥x∥22/2)
on Bn
Description
Implementation of the function
f:Bn→[0,∞),x↦f(x)=(2π)n/21exp(−∥x∥22/2)=(2π)n/21exp(−21∑i=1nxi2),
where n∈{1,2,3,…}
is the dimension of the integration domain Bn={x∈Rn:∥x∥2≤1}
.
In this case the integral is know to be
∫Bnf(x)dx=P[Z≤1]=Fχn2(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)
[Package
multIntTestFunc version 0.2.0
Index]