lmomco (version 0.88)

Lcomoment.Wk: 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.

Value

• A single L-comoment weight factor.

source

Serfling and Xiao (2006).

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).

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

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)