Comparison of Generalized Lambda Distribution (GLD) and Response Modeling Methodology (RMM) as General Platforms for Distribution Fitting

Abstract

Distribution fitting is widely practiced in all branches of engineering and applied science, yet only a few studies have examined the relative capability of various parameter-rich families of distributions to represent a wide spectrum of diversely shaped distributions. In this article, two such families of distributions, Generalized Lambda Distribution (GLD) and Response Modeling Methodology (RMM), are compared. For a sample of some commonly used distributions, each family is fitted to each distribution, using two methods: fitting by minimization of the L ₂ norm (minimizing density function distance) and nonlinear regression applied to a sample of exact quantile values (minimizing quantile function distance). The resultant goodness-of-fit is assessed by four criteria: the optimized value of the L ₂ norm, and three additional criteria, relating to quantile function matching. Results show that RMM is uniformly better than GLD. An additional study includes Shore's quantile function (QF) and again RMM is the best performer, followed by Shore's QF and then GLD.

Keywords:

• Distribution fitting
• Empirical modeling
• Generalized Lambda Distribution
• Response Modeling Methodology

Mathematics Subject Classification:

• Primary 62E17
• Secondary 60E05

Acknowledgment

The partial support of the Paul Ivanier Center of Robotics at Ben-Gurion University is acknowledged.

Notes

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