Lcomoment.matrix: 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

The order of the L-comoments to compute. Default is $k = 1$

Value

An R list is returned.
typeThe type of L-comoment representation in the matrix: Lcomoments.
orderThe order of the matrix---specified by k in the argument list.
matrixA kth order L-comoment matrix.

source

Serfling and Xiao (2006).

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

$\boldmath Λ_{k} = ({\hat{λ}}_{k [i j]})$

computed over the pairs ($X^{(i)},X^{(j)}$) where $1 \le i \le j \le d$.

References

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

Examples

Run this code

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

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