Description Usage Arguments Value Note Author(s) References See Also Examples

A sample trimmed L-moment (TL-moment) is computed for a vector. The *r ≥ 1* order of the L-moment is specified as well as the level of symmetrical trimming. A trimmed TL-moment
*\hat{λ}^{(t_1,t_2)}_r* is

* \hat{λ}^{(t_1,t_2)}_r = \frac{1}{r}∑^{n-t_2}_{i=t_1+1}
≤ft[ \frac{∑\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} ≤ x_{2:n} ≤ … ≤ x_{n:n}*).

1 |

`x` |
A vector of data values. |

`order` |
L-moment order to use in the computations. Default is 1 (the mean). |

`trim` |
Level of symmetrical trimming to use in the computations. Although |

`leftrim` |
Level of trimming of the left-tail of the sample, which should be left to |

`rightrim` |
Level of trimming of the right-tail of the sample, which should be left to |

`sortdata` |
A logical switch on whether the data should be sorted. The default is TRUE. |

An **R** `list`

is returned.

`lambda` |
The TL-moment of order= |

`order` |
L-moment order computed. Default is 1 (the mean). |

`trim` |
Level of symmetrical trimming used in the computation. |

`leftrim` |
Level of left-tail trimming used in the computation, which will equal |

`rightrim` |
Level of right-tail trimming used in the computation, which will equal |

The presence of the `sortdata`

switch can be dangerous. L-moment computation requires that the data be sorted into the “order statistics”. Thus the default behavior of `sortdata=TRUE`

is required when the function is called on its own. In practice, this function would almost certainly not be used on its own because multiple trimmed L-moments would be needed. Multiple trimmed L-moments are best computed by `TLmoms`

, which calls `TLmom`

multiple times. The function `TLmoms`

takes over the sort operation on the data and passes `sortdata=FALSE`

to `TLmom`

for efficiency. (The point of this discussion is that CPU time is not wasted sorting the data more than once.)

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.

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