Comparison of GLD Fitting Methods: Superiority of Percentile Fits to Moments in L^2 Norm

The flexibility of the family of Generalized Lambda Distributions (GLD) has encouraged researchers to fit GLD distributions to datasets in many circumstances. The methods that have been used to obtain GLD fits have also varied. This paper compares, for the first time, the relative qualities of three GLD fitting methods: the method of moments, a method based on percentiles, and a method that uses L-moments.