Calculate moments of the FKML type of the generalised lambda distribution for given parameter values
Calculates the mean, variance, skewness ratio and kurtosis ratio of the generalised lambda distribution for given parameter values.
gld.moments(par,type="fkml",ratios=TRUE)
par |
A vector of length 4, giving the parameters of the generalised lambda distribution, consisting of; lambda 1 location parameter lambda 2 - scale parameter lambda 3 - first shape parameter lambda 4 - second shape parameter |
type |
choose the type of generalised lambda distribution. Currently |
ratios |
Logical. TRUE to give moment ratios for skewness and kurtosis, FALSE to give the third and fourth central moments instead. |
The FKML type of the generalised lambda distribution was introduced by Freimer et al (1988) who gave expressions for the moments. In the limit, as the shape parameters (lambda 3 and lambda 4) go to zero, the distribution is defined using limit results. The moments in these limiting cases were given by van Staden (2013). This function calculates the first 4 moments.
See pages 96–97 of van Staden (2013) for the full expressions for these moments.
A vector containing the first four moments of the FKML type generalized
lambda. If ratio is true, the vector contains the mean,
variance, skewness ratio and kurtosis ratio. If ratio is false,
the vector contains the mean, variance, third central moment and fourth
central moment.
Sigbert Klinke
Paul van Staden
Au-Yeung, Susanna W. M. (2003) Finding Probability Distributions From Moments, Masters thesis, Imperial College of Science, Technology and Medicine (University of London), Department of Computing https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.106.6130&rep=rep1&type=pdf
Freimer, M., Kollia, G., Mudholkar, G. S., & Lin, C. T. (1988), A study of the generalized tukey lambda family, Communications in Statistics - Theory and Methods 17, 3547–3567.
Lakhany, Asif and Mausser, Helmut (2000) Estimating the parameters of the generalized lambda distribution, Algo Research Quarterly, 3(3):47–58
van Staden, Paul J. (2013) Modeling of generalized families of probability distributions inthe quantile statistical universe, PhD thesis, University of Pretoria. https://repository.up.ac.za/handle/2263/40265
gld.moments(c(0,1.463551,0.1349124,0.1349124)) gld.moments(c(0,1.813799,0,0)) gld.moments(c(0,1,0,3))
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