TLmom {lmomco} | R Documentation |
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}).
TLmom(x,order,trim=NULL,leftrim=NULL,rightrim=NULL,sortdata)
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. |
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. |
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.)
W.H. Asquith
Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational statistics and data analysis, vol. 43, pp. 299-314.
X1 <- rcauchy(30) TL <- TLmom(X1,order=2,trim=1)