varLmoments {nsRFA}

Exact variance structure of sample L-moments

Description

varLmoments provides distribution-free unbiased estimators of the variances and covariances of sample L-moments.

Usage

 varLmoments (x, matrix=TRUE)
 varLCV (x)
 varLCA (x)
 varLkur (x)

Arguments

x

vector representing a data-sample

matrix

if TRUE (default), the matrix of estimates of the variance structure (variance and covariance) i of sample L-moments is returned; if FALSE, a vector containing var(l_1), var(l_2), var(l_3), var(l_4), var(t), var(t_3) and var(t_4) is returned.

Details

The estimation of the exact variance structure of sample L-moments is based on Elamir et Seheult (2004).

Value

varLmoments gives the matrix of unbiased estimates of the variance structure of sample L-moments: this is a 4x4 matrix containg var(l_1), var(l_2), var(l_3), var(l_4) on the main diagonal, and the correspondant covariances elsewhere (cov(l_1,l_2), cov(l_1,l_3), etc.);

varLCV gives the unbiased estimate of the variance of sample coefficient of L-variation of x;

varLCA gives the unbiased estimate of the variance of sample L-skewness of x;

varLkur gives the unbiased estimate of the variance of sample L-kurtosis of x.

Note

For information on the package and the Author, and for all the references, see nsRFA.

See Also

var, Lmoments.

Examples

x <- rnorm(30,10,2)
varLmoments(x)
varLmoments(x, FALSE)

varLCV(x)
varLCA(x)
varLkur(x)

data(hydroSIMN)
x <- annualflows["dato"][,]
cod <- annualflows["cod"][,]
dvarLmom <- function(x) {diag(varLmoments(x))}
sapply(split(x,cod),dvarLmom)