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lmomco (version 1.4.3)

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.

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., 2007, A contribution to multivariate L-moments---L-comoment matrices: Journal of Multivariate Analysis, v.~98, pp.~1765--1781.

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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