lmomco (version 0.6)

Lcomoment.coefficients: L-comoment Coefficient Matrix

Description

Compute the L-comoment coefficients from an L-comoment matrix of order $k \ge 2$ and the $k = 2$ (2nd order) L-comoment matrix. This function requires that each matrix is already computed by the function Lcomoment.matrix.

Usage

Lcomoment.coefficients(Lk,L2)

Arguments

Lk

A $k \ge 2$ L-comoment matrix from Lcomoment.matrix.

L2

A $k = 2$ L-comoment matrix from Lcomoment.matrix(Dataframe,k=2).

Value

• An R list is returned.
• type
  The type of L-comoment representation in the matrix: Lcomoment.coefficients.
• order
  The order of the matrix--extracted from the first matrix in arguments.
• matrix
  A $k \ge 2$ L-comoment coefficient matrix.

source

Serfling and Xiao (2006).

Details

L-correlation is computed by Lcomoment.coefficients(L2,L2) where L2 is a $k = 2$ L-comoment matrix. L-coskew, L-cokurtosis, and so on are computed by the function Lcomoment.coefficients(L3,L2), Lcomoment.coefficients(L4,L2), and so on. The usual univariate L-moments as seen from lmom.ub are along the diagonal. This function does not make use of lmom.ub. The L-correlation is computed by extraction of the diagonal and dividing each row in the matrix by the corresponding value from the diagonal.

References

Serfling, R., and Xiao, P., 2006, Multivariate L-moments, preprint.

See Also

lmom.ub, Lcomoment.matrix, Lcomoment.coefficients

Examples

D      <- data.frame(X1=rnorm(30),X2=rnorm(30),X3=rnorm(30))
L2     <- Lcomoment.matrix(D,k=2)
L3     <- Lcomoment.matrix(D,k=3)
LkTAU3 <- Lcomoment.coefficients(L3,L2)