Lcomoment.matrix {lmomco}R Documentation

Compute Sample L-comoment Matrix

Description

Compute the L-comoments from a rectangular data.frame contain arrays of random variables. The order of the L-comoments is specified.

Usage

Lcomoment.matrix(DATAFRAME,k=1)

Arguments

DATAFRAME A convential data.frame that is rectangular
k The order of the L-comoments to compute. Default is k = 1

Details

L-comoments are computed for each item in the data.frame. L-comoments of order k = 1 are means and comeans. L-coments of order k = 2 are L-scale and L-coscale values. L-comoments of order k = 3 are L-skew and L-coskews. L-comoments of order k = 4 are L-kurtosis and L-cokurtosis, and so on. The usual univariate L-moments of order k as seen from lmom.ub are along the diagonal. This function does not make use of lmom.ub. The Lcomoment.matrix function calls Lcomment.Lk12 for each cell in the matrix. The L-comoment matrix for d-random variables is

mbox{boldmath $Lambda_k$} = (hat{λ}_{k[ij]})

computed over the pairs (X^{(i)},X^{(j)}) where 1 <= i <= j <= d.

Value

An R list is returned.

type The type of L-comoment representation in the matrix: “Lcomoments”.
order The order of the matrix—specified by k in the argument list.
matrix A kth order L-comoment matrix.

Note

The function begins with a capital letter. This is intentionally done so that lower case namespace is preserved. L-comoments are new in the literature and experimental in this package. By using a capital letter now, then lcomoment.matrix remains an available name in future releases.

Author(s)

W.H. Asquith

References

Serfling, R., and Xiao, P., 2007, A contribution to multivariate L-moments—L-comoment matrices: Journal of Multivariate Analysis, v.~98, pp.~1765–1781.

See Also

Lcomoment.Lk12, Lcomoment.coefficients, lmom.ub

Examples

D  <- data.frame(X1=rnorm(30),X2=rnorm(30),X3=rnorm(30))
L1 <- Lcomoment.matrix(D,k=1)
L2 <- Lcomoment.matrix(D,k=2)

[Package lmomco version 0.96.3 Index]