Recursive function to compute a multivariate moment

Description

Called by callmultmoments to compute representation of a multivariate normal moment using recursive algorithm

Usage

1
multmoments(moment,current.matrix,current.cell,moment.rep,row_col)

Arguments

moment

vector c(k1,...,kn) specifying the moment X1**k1 *...* Xn**kn

current.matrix

upper-triangular integer matrix under consideration in recursion

current.cell

cell in current matrix under consideration in recursion

moment.rep

current set of representations; mult.moments adds each satisfying matrix to moment.rep

row_col

matrix giving rows and columns for square matrix for each cell

Details

Each row of the representation gives the exponents for a single product of covariance terms. For example, (1,2,0) represents S11**1 S12**2 S22**0, where the Sij are the covariances.

This function would normally only be called by callmultmoments.

Value

moment representation, moment.rep, augmented with additional representations

Author(s)

Kem Phillips <kemphillips@comcast.net>

References

K Phillips, Symbolic Computation of the Central Moments of the Multivariate Normal Distribution, Journal of Statistical Software, 2010.

See Also

callmultmoments (symmoments)