Fitting the Generalized Lambda Distribution with Location and Scale-Free Shape Functionals

Synoptic Abstract

The generahzed lambda distribution (gld) is a family of distributions that can take on a very wide range of shapes within one distributional form. We present a fitting method for the gld using location and scale-free shape functionals to fit the shape functions before fitting the location and scale parameters. Such functions provide an alternative to the moments as a “shape-first” approach, with the advantage of being defined for parameter values where moments are infinite. We investigate the performance of the method with a simulation study and illustrate its use to choose parameter values of the gld to approximate other distributions.

Key Words and Phrases:

• Shape Functionals
• Generalized Lambda Distribution
• Ratio of spread functions