Lcomoment.Wk {lmomco}R Documentation

Weighting Coefficient for Sample L-comoment

Description

Compute the weight factors for computation of an L-comoment for order k, order statistic r, and sample size n.

Usage

Lcomoment.Wk(k,r,n)

Arguments

k Order of L-comoment being computed by parent calls to Lcomoment.Wk.
r Order statistic index involved.
n Sample size.

Details

This function computes the weight factors needed to calculation L-comoments and is interfaced or used by Lcomoment.Lk12. This function is not necessarily for end users. The weight factor w^{(k)}_{r:n} is the discrete Legendre polynomial. The weight factors are well illustrated in figure 2.6 of Hosking and Wallis (1997).

w^{(k)}_{r:n} = sum_{j=0}^{min{r-1,k-1}} (-1)^{k-1-j} frac{{k-1 choose j}{k-1+j choose j} {r-1 choose j}} {{n-1 choose j}} mbox{.}

Value

A single L-comoment weight factor.

Note

The function begins with a capital letter. This is intentionally done so that lower case namespace is preserved. L-comoments are new in the literature and experimental in this package. By using a capital letter now, then lcomoment.Wk remains an available name in future releases.

Author(s)

W.H. Asquith

Source

Serfling and Xiao (2006).

References

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

Serfling, R., and Xiao, P., 2006, Multivariate L-moments, preprint.

See Also

Lcomoment.Wk

Examples

Wk <- Lcomoment.Wk(2,3,5)
# To compute the weight factors for L-skew and L-coskew (k=3) computation
# for a sample of size 20.
Wk <- matrix(nrow=20,ncol=1)
for(r in seq(1,20)) Wk[r] <- Lcomoment.Wk(3,r,20)
# plot(seq(1,20),Wk)

[Package lmomco version 0.96 Index]