Lcomoment.Wk {lmomco} | R Documentation |
Compute the weight factors for computation of an L-comoment for order k
,
order statistic r
, and sample size n
.
Lcomoment.Wk(k,r,n)
k |
Order of L-comoment being computed by parent calls to Lcomoment.Wk . |
r |
Order statistic index involved. |
n |
Sample size. |
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{.}
A single L-comoment weight factor.
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.
W.H. Asquith
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., 2007, A contribution to multivariate L-moments—L-comoment matrices: Journal of Multivariate Analysis, v.~98, pp.~1765–1781.
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)