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 \(i\)th sample order statistic (\(x_{1:n} \le x_{2:n} \le \dots \le x_{n:n}\)).
TLmom(x, order, trim=NULL, leftrim=NULL, rightrim=NULL, sortdata=TRUE)An R
list is returned.
The TL-moment of order=order, \(\hat{\lambda}^{(t_1,t_2)}_r\) where \(r\) is the moment order, \(t_1\) is left-tail trimming, and \(t_2\) is right-tail trimming.
L-moment order computed. Default is 1 (the mean).
Level of symmetrical trimming used in the computation.
Level of left-tail trimming used in the computation, which will equal trim if symmetrical trimming was used.
Level of right-tail trimming used in the computation, which will equal trim if symmetrical trimming was used.
A vector of data values.
L-moment order to use in the computations. Default is 1 (the mean).
Level of symmetrical trimming to use in the computations. Although NULL is in the argument list, the default is 0---the usual L-moment is returned.
Level of trimming of the left-tail of the sample, which should be left to NULL if no or symmetrical trimming is used.
Level of trimming of the right-tail of the sample, which should be left to NULL if no or symmetrical trimming is used.
A logical switch on whether the data should be sorted. The default is TRUE.
W.H. Asquith
Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, v. 43, pp. 299--314.
TLmoms
X1 <- rcauchy(30)
TL <- TLmom(X1,order=2,trim=1)
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