lmomco (version 1.4.3)

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

k

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

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.

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

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

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

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)