Fitting the generalized lambda distribution to data: a method based on percentiles

Abstract

The generalized lambda distribution, GLD(λ₁:,λ₂:,λ₃:,λ₄), is a four‐parameter family that has been used for fitting distributions to a wide variety of data sets. In almost all cases the method of moments has been used to determine the parameters of the GLD that fits a given data set, negating the possibility of applying those members of the GLD family that do not possess the first four moments and yet may provide superior fits to the data. This paper develops a method for fitting a GLD distribution to data that is based on percentiles rather than moments. This approach makes a larger portion of the GLD family accessible for data fitting and eases some of the computational difficulties encountered in the method of moments. Examples of the use of the proposed system are included.

Keywords:

• data fitting
• generalized lambda distribution
• generalized beta distribution
• system of probability distributions
• method of moments
• method of percentiles