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Abstract:
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Generalized Lambda Distribution (GLD) has been highly prized in financial data analysis for its flexibility. With one location, one scale and two shape parameters, it is adaptable to various distribution shapes, especially ones with heavy tails that cannot be fitted with many other commonly used distributions, including normal distribution. Despite its desirable features, GLD's complex parameterization has caused difficulties in data fitting, hence hampered its practicality. Existing fitting methods include Method of Moments, Method of Percentiles, Maximum Likelihood Estimation and Starship, all of which apply to limited parameter space with high computational cost. Here we propose an improved two-step fitting algorithm resulting in wider applicability, faster computation, and higher accuracy. Step one derives from the Method of Robust Moment, and provides a list of possible parameter estimates using a coarse searching grid. Step two screens through all estimate candidates, and chooses the best set by comparing empirical and estimated quantiles. Aside from its technical merits, our new algorithm is deemed to be more user-friendly with easy comprehensibility and customizability.
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