R: L-moments

Lmoments {Lmoments} | R Documentation

## L-moments

### Description

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

### Usage

    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.

`Lmoments_calc` is an internal function.

`Lmomcov_calc` is an internal function.

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

### Note

Functions `Lmoments` and `Lcoefs` calculate trimmed L-moments if you specify `trim=c(1,1)`.

### Author(s)

Juha Karvanen juha.karvanen@iki.fi

### 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.

### See Also

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

### Examples

    #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');

[Package Lmoments version 1.2-3 Index]