Estimation and Use of the Generalised (Tukey) Lambda Distribution

The generalised lambda distribution, or Tukey lambda distribution, provides a wide variety of shapes with one functional form. This package provides random numbers, quantiles, probabilities, densities and density quantiles for four different types of the distribution, the FKML (Freimer et al 1988), RS (Ramberg and Schmeiser 1974), GPD (van Staden and Loots 2009) and FM5 - see documentation for details. It provides the density function, distribution function, and Quantile-Quantile plots. It implements a variety of estimation methods for the distribution, including diagnostic plots. Estimation methods include the starship (all 4 types), method of L-Moments for the GPD and FKML types, and a number of methods for only the FKML type. These include maximum likelihood, maximum product of spacings, Titterington's method, Moments, Trimmed L-Moments and Distributional Least Absolutes.


2.5 (to come ...) Standard Errors for the L Moment estimates for the GPD type

2.4.2 Fix bug in fit.gpd BetaLambdaLambda function added (utility function for gpd L-Moment estimation)

2.4.1 Fix pgl() example comment - inverse.eps had defaulted to .Machine$double.eps since version 1.9

2.4 L Moment estimation for the GPD type

2.3.3 print.starship, summary.starship and plot.starship now display estimation method and gld type

2.3 Moment estimation for FKML type qdgl function deprecated in favour of dqgl as it calculates the density quantile function of the gld

2.2 New estimation methods for the FKML parameterisation: Numerical MLE, Maximum Spacings Product, Titteringtons, L Moments, TL Moments, Distributional Least Absolutes Starship has C speedups from Ben Dean, in fit.fkml function

Reference manual

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2.6.2 by Robert King, 2 years ago

Browse source code at

Authors: Robert King <[email protected]> , Benjamin Dean <[email protected]> , Sigbert Klinke , Paul van Staden

Documentation:   PDF Manual  

Task views: Probability Distributions

GPL (>= 2) license

Imports stats, graphics, e1071, lmom

Imported by DescTools.

Depended on by PairedData.

Suggested by GenHMM1d, fitteR, glmx.

See at CRAN