lmomco (version 2.3.1)

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 been 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.

type

The type of L-comoment representation in the matrix: “Lcomoment.coefficients”.

order

The order of the coefficients. order=2 L-covariation, order=3 L-coskew, …

matrix

A \(k \ge 2\) 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 for \(k \ge 3\) are

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

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

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.

See Also

Lcomoment.matrix, Lcomoment.coefficients

Examples

# NOT RUN {
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)
# }