$$\hat{\lambda}^{(t_1,t_2)}_r = \frac{1}{r}\sum^{n-t_2}_{i=t_1+1} \left[ \frac{\sum\limits^{r-1}_{k=0}{ (-1)^k {r-1 \choose k} {i-1 \choose r+t_1-1-k} {n-i \choose t_2+k} }}{{n \choose r+t_1+t_2}} \right] x_{i:n} \mbox{,}$$
where $t$ 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 ($x_{1:n} \le x_{2:n} \le \dots \le x_{n:n}$). This function loops across the above equation for each nmom set in
the argument list.
TLmoms(x,nmom,trim=NULL,leftrim=NULL,rightrim=NULL)NULL if asymmetrical trimming was used. Although NULL in the argument list, the default is 0---the usual L-moment is returned.list is returned.NULL if asymmetrical trimming was used.TLmom, lmoms, and lmorphX1 <- rcauchy(30)
TL <- TLmoms(X1,nmom=6,trim=1)Run the code above in your browser using DataLab