# t1lmoments: Trimmed L-moments In Lmoments: L-Moments and Quantile Mixtures

## Description

Calculates sample trimmed L-moments with trimming parameter 1.

## Usage

 ```1 2``` ```t1lmoments(data, rmax = 4) t1lmoments_calc(data, rmax = 4) ```

## Arguments

 `data` matrix or data frame. `rmax` maximum order of trimmed L-moments.

## Value

array of trimmed L-moments (trimming parameter = 1) up to order 4 containing a row for each variable in data.

## Note

Functions `link{Lmoments}` and `link{Lcoefs}` calculate trimmed L-moments if you specify `trim = c(1, 1)`. `t1lmoments_calc` is an internal C++ function called by `t1lmoments`. The direct use of this function is not recommended.

## Author(s)

Juha Karvanen juha.karvanen@iki.fi, Santeri Karppinen

## References

Karvanen, J. 2006. Estimation of quantile mixtures via L-moments and trimmed L-moments, Computational Statistics & Data Analysis 51, (2), 947–959. http://www.bsp.brain.riken.jp/publications/2006/karvanen_quantile_mixtures.pdf.

Elamir, E. A., Seheult, A. H. 2003. Trimmed L-moments, Computational Statistics & Data Analysis 43, 299–314.

`Lmoments` for L-moments, and `dcauchypoly` and `t1lmom2cauchypoly4` for the Cauchy-polynomial quantile mixture

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```#Generates 500 random variables from the Cauchy-polynomial quantile mixture, #calculates the trimmed L-moments, #estimates parameters via trimmed L-moments and #plots the true pdf and the estimated pdf together with the histogram of the data. true_params<-t1lmom2cauchypoly4(c(0,1,0.075,0.343)); x<-rcauchypoly(500,true_params); t1lmom<-t1lmoments(x); estim_params<-t1lmom2cauchypoly4(t1lmom); plotpoints<-seq(-10,10,by=0.01); histpoints<-c(seq(min(x)-1,-20,length.out=50),seq(-10,10,by=0.5),seq(20,max(x)+1,length.out=50)); hist(x,breaks=histpoints,freq=FALSE,xlim=c(-10,10)); lines(plotpoints,dcauchypoly(plotpoints,estim_params),col='red'); lines(plotpoints,dcauchypoly(plotpoints,true_params),col='blue'); ```

### Example output

```
```

Lmoments documentation built on May 2, 2019, 2:04 a.m.