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)

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 internal function.
Lmomcov_calc is internal function.

Note

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

Author(s)

Juha Karvanen <juha.karvanen@ktl.fi>

References

Karvanen, J. 2005. Estimation of quantile mixtures via L-moments and trimmed L-moments, Computational Statistics & Data Analysis, in press, http://www.bsp.brain.riken.jp/publications/2005/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 1.1-2 Index]