varLmoments {nsRFA} | R Documentation |
varLmoments
provides distribution-free unbiased estimators of the variances and covariances of sample L-moments.
varLmoments (x, matrix=TRUE) varLCV (x) varLCA (x) varLkur (x)
x |
vector representing a data-sample |
matrix |
if TRUE (default), the matrix of estimates of the variance structure (variance and covariance) 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. |
The estimation of the exact variance structure of sample L-moments is based on Elamir et Seheult (2004)
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
.
Alberto Viglione, e-mail: alviglio@tiscali.it.
Elamir, E.A.H. and Seheult, A.H. (2004) Exact variance structure of sample L-moments, Journal of Statistical Planning and Inference 124, 337-359.
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)