# TLmoms: The Sample Trimmed L-moments and L-moment Ratios In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

Compute the sample trimmed L-moments (TL-moments) for a vector. The level of symmetrical trimming is specified. The mathematical expression for a TL-moment is seen under TLmom. The TLmoms function loops across that expression and the TLmom function for each nmom=r set in the argument list.

## Usage

 1 TLmoms(x, nmom, trim=NULL, leftrim=NULL, rightrim=NULL, vecit=FALSE) 

## 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. Although NULL is 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, which should be left to NULL if no or symmetrical trimming is used. rightrim Level of trimming of the right-tail of the sample, which should be left to NULL if no or symmetrical trimming is used. vecit A logical to return the first two λ_i \in 1,2 and then the τ_i \in 3,\cdots where the length of the returned vector is controlled by the nmom argument. This argument will store the trims in the attributes of the returned vector, but caution is advised if vec2par were to be used on the vector because that function does not consult the trimming.

## 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{τ}^{(t_1,t_2)}, third element is \hat{τ}^{(t_1,t_2)}_3 and so on. trim Level of symmetrical trimming used in the computation. leftrim Level of left-tail trimming used in the computation, which will equal trim if symmetrical trimming was used. rightrim Level of right-tail trimming used in the computation, which will equal trim if symmetrical trimming was used. source An attribute identifying the computational source of the L-moments: “TLmoms”.

W.H. Asquith

## References

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

TLmom, lmoms, and lmorph
  1 2 3 4 5 6 7 8 9 10 11 X1 <- rcauchy(30) TL <- TLmoms(X1,nmom=6,trim=1) # This trimming with remove the 1 and the two 4s. All values passed on to the TLmom() # function then are equal and number of L-moments is too big as well. TLmom() returns # NaN but these are intercepted and systematically changed to NAs. TLmoms(c(1,2,2,2,4,4), leftrim=1, rightrim=2, nmom=6)\$lambdas # [1] 2 0 0 NA NA NA # Example of zero skewness (Berry Boessenkool) TLmoms(c(3.2, 4.4, 4.8, 2.6, 3.6))