Pn_lognormalDensity-class {multIntTestFunc}

An S4 class to represent the function \frac{1}{(\prod_{i=1}^{n}x_i) \sqrt{(2\pi)^n\det(\Sigma)}}\exp(-((\ln(\vec{x})-\vec{\mu})^{T}\Sigma^{-1}(\ln(\vec{x})-\vec{\mu}))/2) on [0,\infty)^n

Description

Implementation of the function

f \colon R^n \to [0,\infty),\, \vec{x} \mapsto f(\vec{x}) = \frac{1}{(\prod_{i=1}^{n}x_i) \sqrt{(2\pi)^n\det(\Sigma)}}\exp(-((\ln(\vec{x})-\vec{\mu})^{T}\Sigma^{-1}(\ln(\vec{x})-\vec{\mu}))/2),

where n \in \{1,2,3,\ldots\} is the dimension of the integration domain [0,\infty)^n = \times_{i=1}^n [0,\infty). In this case the integral is know to be

\int_{R^n} f(\vec{x}) d\vec{x} = 1.

Details

The instance needs to be created with three parameters representing the dimension n, the location vector \vec{\mu} and the variance-covariance matrix \Sigma which needs to be symmetric positive definite.

Slots

dim

An integer that captures the dimension

mean

A vector of size dim with real entries.

sigma

A matrix of size dim x dim that is symmetric positive definite.

Author(s)

Klaus Herrmann

Examples

n <- as.integer(3)
f <- new("Pn_lognormalDensity",dim=n,mean=rep(0,n),sigma=diag(n))