TLmoms {lmomco} | R Documentation |
Compute the sample trimmed L-moments (TL-moments) for a vector. The level of symmetrical trimming is specified. A TL-moment is
hat{λ}^{(t_1,t_2)}_r = frac{1}{r}sum^{n-t_2}_{i=t_1+1} <=ft[ frac{sumlimits^{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-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}). This function loops across the above equation for each nmom
set in
the argument list.
TLmoms(x,nmom,trim=NULL,leftrim=NULL,rightrim=NULL)
x |
A vector of data values. |
nmom |
The number of moments to compute. Default is 5. |
trim |
Level of symmetrical trimming to use in the computations, which will equal NULL if asymmetrical trimming was used. 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. |
An R list
is returned.
lambdas |
Vector of the TL-moments. First element is hat{λ}^{(t_1,t_2)}_1, second element is hat{λ}^{(t_1,t_2)}_2, and so on. |
ratios |
Vector of the L-moment ratios. Second element is hat{tau}^{(t_1,t_2)}, third element is hat{tau}^{(t_1,t_2)}_3 and so on. |
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. |
source |
An attribute identifying the computational source of the L-moments: “TLmoms”. |
It is important to note that the “L-moment object” returned by TLmoms
is different in structure to that returned by lmom.ub
, pwm2lmom
, and similar as the TL-moments should not be confused with the ordinary L-moments. Implementation in the package might change.
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 <- TLmoms(X1,nmom=6,trim=1)