| TLmom {lmomco} | R Documentation |
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
\hat{\lambda}^{(t_1,t_2)}_r is
\hat{\lambda}^{(t_1,t_2)}_r = \frac{1}{r}\sum^{n-t_2}_{i=t_1+1}
\left[ \frac{\sum\limits^{r-1}_{k=0}{ (-1)^k {r-1 \choose k}
{i-1 \choose r+t_1-1-k}
{n-i \choose t_2+k}
}}{{n \choose r+t_1+t_2}}
\right] x_{i:n} \mbox{,}
where t_a represents the trimming level of the t_2-largest or t_1-smallest values, r represents the order of the L-moment, n represents the sample size, and x_{i:n} represents the ith 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=TRUE)
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 |
leftrim |
Level of trimming of the left-tail of the sample, which should be left to |
rightrim |
Level of trimming of the right-tail of the sample, which should be left to |
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 |
L-moment order computed. Default is 1 (the mean). |
trim |
Level of symmetrical trimming used in the computation. |
leftrim |
Level of left-tail trimming used in the computation, which will equal |
rightrim |
Level of right-tail trimming used in the computation, which will equal |
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 almost certainly not be used on its own because 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 CPU time is not wasted 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, v. 43, pp. 299–314.
See Also
Examples
X1 <- rcauchy(30)
TL <- TLmom(X1,order=2,trim=1)