TLmom {lmomco}R Documentation

A Sample Trimmed L-moment

Description

A sample trimmed L-moment (TL-moment) is computed for a vector. The r >= 1 order of the L-moment is specified as well as the level of symmetrical trimming. A trimmed TL-moment is

hat{λ}^{(t)}_r = frac{1}{r}sum^{n-t}_{i=t+1} <=ft[ frac{sumlimits^{r-1}_{k=0}{ (-1)^k {r-1 choose k} {i-1 choose r+t-1-k} {n-i choose t+k} }}{{n choose r+2t}} right] x_{i:n} mbox{,}

where t represents the trimming level of the t-largest or t-smallest values, r represents the order of the L-moments, n represents the sample size, and x_{i:n} represents the ith sample order statistic (x_{1:n} <= x_{2:n} <= ... <= x_{n:n}).

Usage

TLmom(x,order,trim=NULL,leftrim=NULL,rightrim=NULL,sortdata)

Arguments

x A vector of data values.
order L-moment order to use in the computations. Default is 1 (the mean).
trim Level of symmetrical trimming to use in the computations. Although NULL in the argument list, the default is 0—the usual L-moment is returned.
leftrim Level of trimming of the left-tail of the sample.
rightrim Level of trimming of the right-tail of the sample.
sortdata A logical switch on whether the data should be sorted. The default is TRUE.

Value

An R list is returned.

lambda The TL-moment of order=order and trimming=trim.
order L-moment order computed. Default is 1 (the mean).
trim Level of symmetrical trimming used in the computation, which will equal NULL if asymmetrical trimming was used.
leftrim Level of left-tail trimming used in the computation.
rightrim Level of right-tail trimming used in the computation.

Note

The presence of the sortdata switch can be dangerous. L-moment computation requires that the data be sorted into the “order statistics”. Thus the default behavior of sortdata=TRUE is required when the function is called on its own. In practice, this function would not be used as multiple trimmed L-moments would be needed. Multiple trimmed L-moments are best computed by TLmoms, which calls TLmom multiple times. The function TLmoms takes over the sort operation on the data and passes sortdata=FALSE to TLmom for efficiency. (The point of this discussion is that one does not want to waste CPU time sorting the data more than once.)

Author(s)

W.H. Asquith

References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational statistics and data analysis, vol. 43, pp. 299-314.

See Also

TLmoms

Examples

X1 <- rcauchy(30)
TL <- TLmom(X1,order=2,trim=1)

[Package lmomco version 0.96.3 Index]