# Lcomoment.matrix: Compute Sample L-comoment Matrix In wasquith/lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

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

## Usage

 1 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 co-means. L-comoments 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 or lmoms are along the diagonal. This function does not make use of lmom.ub or lmoms. The function Lcomoment.matrix calls Lcomoment.Lk12 for each cell in the matrix. The L-comoment matrix for d-random variables is

\mbox{\boldmath $Λ_k$} = (\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. By using a capital letter now, then lcomoment.matrix remains an available name in future releases.

W.H. Asquith

## References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

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

Lcomoment.Lk12, Lcomoment.coefficients
 1 2 3 D <- data.frame(X1=rnorm(30), X2=rnorm(30), X3=rnorm(30)) L1 <- Lcomoment.matrix(D,k=1) L2 <- Lcomoment.matrix(D,k=2)