Lmoments {Lmoments}

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. 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 [e-mail], 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.

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');