lmomco (version 0.88)

TLmom: A Sample Trimmed L-moment

Description

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

$$\hat{\lambda}^{(t)}_r = \frac{1}{r}\sum^{n-t}_{i=t+1} \left[ \frac{\sum\limits^{r-1}_{k=0}{ (-1)^k {r-1 \choose k} {i-1 \choose r+t-1-k} {n-i \choose t+k} }}{{n \choose r+2t}} \right] x_{i:n} \mbox{,}$$

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 $i$th sample order statistic ($x_{1:n} \le x_{2:n} \le \dots \le x_{n:n}$).

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.

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)