lmomco (version 2.2.5)

Lcomoment.correlation: L-correlation Matrix (L-correlation through Sample L-comoments)

Description

Compute the L-correlation from an L-comoment matrix of order $k = 2$. This function assumes that the 2nd order matrix is already computed by the function Lcomoment.matrix.

Usage

Lcomoment.correlation(L2)

Arguments

L2

A $k = 2$ L-comoment matrix from Lcomoment.matrix(Dataframe,k=2).

Value

An R list is returned.

Details

L-correlation is computed by Lcomoment.coefficients(L2,L2) where L2 is second order L-comoment matrix. The usual L-scale values as seen from lmom.ub or lmoms are along the diagonal. This function does not make use of lmom.ub or lmoms and can be used to verify computation of $\tau$ (coefficient of L-variation).

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.correlation

Examples

D   <- data.frame(X1=rnorm(30), X2=rnorm(30), X3=rnorm(30))
L2  <- Lcomoment.matrix(D,k=2)
RHO <- Lcomoment.correlation(L2)
## Not run: 
# "SerfXiao.eq17" <-
#  function(n=25, A=10, B=2, k=4,
#           method=c("pearson","lcorr"), wrt=c("12", "21")) {
#    method <- match.arg(method); wrt <- match.arg(wrt)
#    # X1 is a linear regression on X2
#    X2 <- rnorm(n); X1 <- A + B*X2 + rnorm(n)
#    r12p <- cor(X1,X2) # Pearson's product moment correlation
#    XX <- data.frame(X1=X1, X2=X2) # for the L-comoments
#    T2 <- Lcomoment.correlation(Lcomoment.matrix(XX, k=2))$matrix
#    LAMk <- Lcomoment.matrix(XX, k=k)$matrix # L-comoments of order k
#    if(wrt == "12") { # is X2 the sorted variable?
#       lmr <- lmoms(X1, nmom=k); Lamk <- LAMk[1,2]; Lcor <- T2[1,2]
#    } else {          # no X1 is the sorted variable (21)
#       lmr <- lmoms(X2, nmom=k); Lamk <- LAMk[2,1]; Lcor <- T2[2,1]
#    }
#    # Serfling and Xiao (2007, eq. 17) state that
#    # L-comoment_k[12] = corr.coeff * Lmoment_k[1] or
#    # L-comoment_k[21] = corr.coeff * Lmoment_k[2]
#    # And with the X1, X2 setup above, Pearson corr. == L-corr.
#    # There will be some numerical differences for any given sample.
#    ifelse(method == "pearson",
#              return(lmr$lambdas[k]*r12p - Lamk),
#              return(lmr$lambdas[k]*Lcor - Lamk))
#    # If the above returns a expected value near zero then, their eq.
#    # is numerically shown to be correct and the estimators are unbiased.
# }
# 
# # The means should be near zero.
# nrep <- 2000; seed <- rnorm(1); set.seed(seed)
# mean(replicate(n=nrep, SerfXiao.eq17(method="pearson", k=4)))
# set.seed(seed)
# mean(replicate(n=nrep, SerfXiao.eq17(method="lcorr", k=4)))
# # The variances should nearly be equal.
# seed <- rnorm(1); set.seed(seed)
# var(replicate(n=nrep, SerfXiao.eq17(method="pearson", k=6)))
# set.seed(seed)
# var(replicate(n=nrep, SerfXiao.eq17(method="lcorr", k=6)))
# ## End(Not run)