varLmoments: 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

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.

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.

Details

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

Examples

Run this code

# NOT RUN {
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)

# }