gld (version 2.4.1)

gld.lmoments: Calculate L-Moments of the GPD type generalised lambda distribution for given parameter values

Description

Calculates the first four L-Moments of the GPD type generalised $lambda$ distribution for given parameter values.

Usage

gld.lmoments(pars,order=1:4,ratios=TRUE,type="GPD")

Arguments

pars

A vector of length 4, giving the parameters of the GPD type generalised lambda distribution, consisting of;

• $alpha$ location parameter
• $beta > 0$ scale parameter
• $0 <= delta="" <="1$" skewness="" parameter="" li="">
• $lambda$ kurtosis parameter

order

Integers to select the orders of L-moments to calculate. Currently this function only calculates for orders 1 to 4.

type

choose the type of generalised lambda distribution. Currently gld.lmoments only supports GPD which uses van Staden and Loots (2009) (default).

ratios

Logical. TRUE gives L-moment ratios for skewness and kurtosis ($tau 3$ and $tau 4$) (and all higher orders), FALSE gives the requested L-moments instead.

Value

A vector containing the selected L-moments of the GPD type generalised lambda. If ratio is true, the vector contains L-Moment ratios for orders 3 and over, otherwise all values are L-Moments.

Details

The GPD type generalised $lambda$ distribution was introduced by van Staden and Loots (2009). It has explicit parameters for skewness and kurtosis, and closed form estimates for L-moment estimates of the parameters.

In the limit, as the kurtosis parameter, $lambda$, goes to zero, the distribution approaches the skew logistic distribution of van Staden and King (2013). See the sld package for this distribution.

References

van Staden, P.J. and King, Robert A.R. (2015) The quantile-based skew logistic distribution, Statistics and Probability Letters 96 109--116. http://dx.doi.org/10.1016/j.spl.2014.09.001

van Staden, Paul J. 2013 Modeling of generalized families of probability distribution in the quantile statistical universe. PhD thesis, University of Pretoria. http://hdl.handle.net/2263/40265

Quantile based Skew logistic distribution

http://tolstoy.newcastle.edu.au/rking/SLD/SLD.html

Generalised Lambda Distribution

http://tolstoy.newcastle.edu.au/~rking/gld/

See Also

sld package

Examples

gld.lmoments(c(0,1,0.5,0.23))
gld.lmoments(c(0,1,0,0.23))
gld.lmoments(c(0,1,0.5,0.7))