Lcomoment.coefficients {lmomco} | R Documentation |
Compute the L-comoment coefficients from an L-comoment matrix of order k >= 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
.
Lcomoment.coefficients(Lk,L2)
Lk |
A k >= 2 L-comoment matrix from Lcomoment.matrix . |
L2 |
A k = 2 L-comoment matrix from Lcomoment.matrix(Dataframe,k=2) . |
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{λ}_{2[12]}} {hat{λ}_{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{λ}_{k[12]}} {hat{λ}_{2[12]}} mbox{, for } k >= 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
.
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 >= 2 L-comoment coefficient matrix. |
The function begins with a capital letter. This is intentionally done so that lower case namespace is preserved. L-comoments are new in the literature and experimental in this package. By using a capital letter now, then lcomoment.coefficients
remains an available name in future releases.
W.H. Asquith
Serfling, R., and Xiao, P., 2007, A contribution to multivariate L-moments—L-comoment matrices: Journal of Multivariate Analysis, v.~98, pp.~1765–1781.
lmom.ub
, Lcomoment.matrix
, Lcomoment.coefficients
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)