eprod {mombf} | R Documentation |
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)
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. |
The calculation is based on the computationally efficient approach by Kan (2008).
Expectation of the above-mentioned product
John Cook
Kan R. From moments of sum to moments of product. Journal of Multivariate Analysis 99 (2008), 542-554.
#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])