multmoments: Recursive Function to Compute a Multivariate Moment

In symmoments: Symbolic Central and Noncentral Moments of the Multivariate Normal Distribution

Recursive Function to Compute a Multivariate Moment

Description

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

Usage

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

Arguments

moment	A vector c(k1, ..., kn) specifying the moment X_1^{k_1} \cdots X_n^{k_n}.
current.matrix	Upper-triangular integer matrix under consideration in the recursion.
current.cell	Cell in the current matrix under consideration in the recursion.
moment.rep	Current set of representations; multmoments adds each satisfying matrix to moment.rep.
row_col	Matrix giving rows and columns for a 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 S_{11}^1 S_{12}^2 S_{22}^0, where the S_{ij} are the covariances.

This function would normally only be called by callmultmoments.

Value

The moment representation, moment.rep, augmented with additional representations.

Author(s)

Kem Phillips [e-mail]

References

\insertRef

Phillips2010symmoments

See Also

callmultmoments

symmoments documentation built on May 27, 2026, 9:06 a.m.