multmoments function

Recursive function to compute a multivariate moment

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

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

Arguments

• moment: vector c(k1,...,kn) specifying the moment X1k1 ... Xnkn
• 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 S111 S122 S22**0, where the Sij are the covariances.

This function would normally only be called by callmultmoments.

Returns

moment representation, moment.rep, augmented with additional representations

References

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

Author(s)

Kem Phillips kemphillips@comcast.net

See Also

callmultmoments (symmoments)