The Generalised λ (lambda) Distribution is an extension, first suggested by Ramberg & Schmeiser (1974), of Tukey's λ distribution.
There are two parameterisations of the distribution, both defined by their inverse distribution function. The two inverse distribution functions are here, labelled by the paper that first introduced them.
Ramberg and Schmeiser's | |
Freimer, Mudholkar, Kollia and Lin's* |
Here λ_{1} (lambda 1) is a location parameter, λ_{2} is an inverse scale parameter and λ_{3} and λ_{4} jointly determine the shape (with λ_{3} mostly effecting the left tail and λ_{4} mostly effecting the right tail).
It is of interest because of the wide variety of distributional shapes that it can take on. The java applet on this page shows the probability density function for any combination of parameters.
You need to click in the graph image to get it to update the graph
In case you have difficulties reading the titles on the graphs, they are graphs of the probability density function for the generalised lambda distribution (Ramberg's parameterisation) for the following parameter values: (0,1,.1,.1), (0,1,.05,.5), (0,-5,-.05,-.1) and (0,1,1.4,1.9)
See my publications information section for information on articles and conference papers related to this distribution.
I have written an add-on package for R that provides this distribution. More information is available here.
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