TLmoms {lmomco}R Documentation

The Sample Trimmed L-moments and L-moment Ratios

Description

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.

Usage

TLmoms(x,nmom,trim=NULL,leftrim=NULL,rightrim=NULL)

Arguments

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.

Value

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”.

Note

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.

Author(s)

W.H. Asquith

References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational statistics and data analysis, vol. 43, pp. 299-314.

See Also

TLmom, lmoms, and lmorph

Examples

X1 <- rcauchy(30)
TL <- TLmoms(X1,nmom=6,trim=1)

[Package lmomco version 0.96.3 Index]