eprod function

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

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

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

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.

Details

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

Returns

Expectation of the above-mentioned product

References

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

Author(s)

John Cook

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])