There are two parameterisations of the distribution, both defined in the form of their inverse distribution function:
Ramberg and Schmeiser's
Freimer, Mudholkar, Kollia and Lin's
Here lambda 1 is a location parameter, lambda 2 is a scale paramter and lambda 3 and lambda 4 together determine the shape.
These equations define a function where the parameter u must change between 0 and 1 (expected result of the function of the cumulative distribution). Inside this interval, the functions value makes the way from minus to plus infinity, representing that would be a parameter of the cumulative distribution function. Hence they are turned by 90 degree angle in comparison of the cumulative distribution that one may expect to see. The analytic form of the cumulative distribution function seem difficult to obtain in case of the generalized lambda distribution, and numeric methods must be used instead. The applet both "turns" the function in a proper orientation and computes the derivative, showing the approximate form of that the sample histogram would take.
The Generalised lambda Distribution is an extension of Tukey's lambda distribution. It was first suggested by first suggested Ramberg & Schmeiser in 1974.