mombf (version 3.5.4)

eprod: Expectation of a product of powers of Normal or T random variables

Description

Compute the mean of prod(x)^power when x follows T_dof(mu,sigma) distribution (dof= -1 for multivariate Normal).

Usage

eprod(m, S, power = 1, dof = -1)

Value

Expectation of the above-mentioned product

Arguments

m

Location parameter

S

Scale matrix. For multivariate T with dof>2 the covariance is S*dof/(dof-2). For the multivariate Normal the covariance is S.

power

Power that the product is raised to

dof

Degrees of freedom of the multivariate T. Set to -1 for the multivariate Normal.

Author

John Cook

Details

The calculation is based on the computationally efficient approach by Kan (2008).

References

Kan R. From moments of sum to moments of product. Journal of Multivariate Analysis 99 (2008), 542-554.

Examples

#Check easy independence case
m <- c(0,3); S <- matrix(c(2,0,0,1),ncol=2)

eprod(m, S, power=2)

(m[1]^2+S[1][1])*(m[2]^2+S[2][2])