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lmomco (version 0.88)

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. However, if the first argument is 1st-order then the coefficients of L-covariation are computed. The function requires that each matrix has 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.
  • typeThe type of L-comoment representation in the matrix: Lcomoment.coefficients.
  • orderThe order of the coefficients. order=2 L-covariation, order=3 L-coskew, ...
  • matrixA $k \ge 2$ L-comoment coefficient matrix.

source

Serfling and Xiao (2006).

Details

The coefficient of L-variation is computed by Lcomoment.coefficients(L1,L2) where L1 is a 1st-order L-moment matrix and L2 is a $k = 2$ L-comoment matrix. Symbolically, the coefficient of L-covariation is

$$\hat{\tau}_{[12]} = \frac{\hat{\lambda}_{2[12]}} {\hat{\lambda}_{1[12]}} \mbox{.}$$

The higher L-comoment coefficients (L-coskew, L-cokurtosis, ...) are computed by the function Lcomoment.coefficients(L3,L2) ($k=3$), Lcomoment.coefficients(L4,L2) ($k=4$), and so on. Symbolically, the higher L-comoment coefficients are

$$\hat{\tau}_{k[12]} = \frac{\hat{\lambda}_{k[12]}} {\hat{\lambda}_{2[12]}} \mbox{, for } k \ge 3 \mbox{.}$$

Finally, the usual univariate L-moment ratios as seen from lmom.ub or lmoms are along the diagonal. The Lcomoment.coefficients function does not make use of lmom.ub or lmoms.

References

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

See Also

lmom.ub, Lcomoment.matrix, Lcomoment.coefficients

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)
L3     <- Lcomoment.matrix(D,k=3)
LkLCV  <- Lcomoment.coefficients(L1,L2)
LkTAU3 <- Lcomoment.coefficients(L3,L2)

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