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

## Description

Calculates sample L-moments, L-coefficients and covariance matrix of L-moments.

## Usage

 ```1 2 3 4 5 6``` ```Lmoments(data, rmax = 4, na.rm = FALSE, returnobject = FALSE, trim = c(0, 0)) Lcoefs(data, rmax = 4, na.rm = FALSE, trim = c(0, 0)) Lmomcov(data, rmax = 4, na.rm = FALSE) Lmoments_calc(data, rmax = 4) Lmomcov_calc(data, rmax = 4) shiftedlegendre(rmax) ```

## Arguments

 `data` matrix or data frame. `rmax` maximum order of L-moments. `na.rm` a logical value indicating whether 'NA' values should be removed before the computation proceeds. `returnobject` a logical value indicating whether a list object should be returned instead of an array of L-moments. `trim` c(0, 0) for ordinary L-moments and c(1, 1) for trimmed (t = 1) L-moments

## Value

`Lmoments` returns an array of L-moments containing a row for each variable in data, or if returnobject=TRUE, a list containing

 `lambdas` an array of L-moments `ratios` an array of mean, L-scale and L-moment ratios `trim` the value of the parameter 'trim' `source` a string with value "Lmoments" or "t1lmoments".

`Lcoefs` returns an array of L-coefficients (mean, L-scale, L-skewness, L-kurtosis, ...) containing a row for each variable in data.

`Lmomcov` returns the covariance matrix of L-moments or a list of covariance matrices if the input has multiple columns. The numerical accuracy of the results decreases with increasing `rmax`. With `rmax > 5`, a warning is thrown, as the numerical accuracy of the results is likely less than `sqrt(.Machine\$double.eps)`.

`shiftedlegendre` returns a matrix of the coefficients of the shifted Legendre polynomials up to a given order.

## Note

Functions `Lmoments` and `Lcoefs` calculate trimmed L-moments if you specify `trim = c(1, 1)`. `Lmoments_calc` and `Lmomcov_calc` are internal C++ functions called by `Lmoments` and `Lmomcov`. The direct use of these functions is not recommended.

## Author(s)

Juha Karvanen [email protected], 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. 2004. Exact variance structure of sample L-moments, Journal of Statistical Planning and Inference 124 (2) 337–359.

Hosking, J. 1990. L-moments: Analysis and estimation distributions using linear combinations of order statistics, Journal of Royal Statistical Society B 52, 105–124.

`t1lmoments` for trimmed L-moments, `dnormpoly`, `lmom2normpoly4` and `covnormpoly4` for the normal-polynomial quantile mixture and package lmomco for additional L-moment functions

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```#Generates a sample 500 observations from the normal-polynomial quantile mixture, #calculates the L-moments and their covariance matrix, #estimates parameters via L-moments and #plots the true pdf and the estimated pdf together with the histogram of the data. true_params<-lmom2normpoly4(c(0,1,0.2,0.05)); x<-rnormpoly(500,true_params); lmoments<-Lmoments(x); lmomcov<-Lmomcov(x); estim_params<-lmom2normpoly4(lmoments); hist(x,30,freq=FALSE) plotpoints<-seq(min(x)-1,max(x)+1,by=0.01); lines(plotpoints,dnormpoly(plotpoints,estim_params),col='red'); lines(plotpoints,dnormpoly(plotpoints,true_params),col='blue'); ```

### Example output

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