varLmoments {nsRFA} | R Documentation

## 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(l1), var(l2), var(l3), var(l4), var(t), var(t3) and var(t4) 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(l1), var(l2), var(l3), var(l4) on the main diagonal, and the correspondant covariances elsewhere (cov(l1,l2), cov(l1,l3), 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)

[Package nsRFA version 0.6-9 Index]