Calculate L-Moments of the GPD type generalised lambda distribution for given parameter values
Calculates the first four L-Moments of the GPD type generalised lambda distribution for given parameter values.
gld.lmoments(pars,order=1:4,ratios=TRUE,type="GPD",param=NULL)
pars |
A vector of length 4, giving the parameters of the GPD type generalised lambda distribution, consisting of;
|
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 |
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. |
param |
alias for the type argument. The |
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.
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.
Paul van Staden
van Staden, P.J. and King, Robert A.R. (2015) The quantile-based skew logistic distribution, Statistics and Probability Letters 96 109–116. https://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. https://hdl.handle.net/2263/40265
Van Staden, Paul J., & M.T. Loots. (2009), Method of L-moment Estimation for the Generalized Lambda Distribution. In Proceedings of the Third Annual ASEARC Conference. Callaghan, NSW 2308 Australia: School of Mathematical and Physical Sciences, University of Newcastle.
Quantile based Skew logistic distribution
Generalised Lambda Distribution
sld package
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))
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