L-moments and TL-moments of the generalized lambda distribution

Computational Statistics and Data Analysis



The 4-parameter generalized lambda distribution (GLD) is a flexible distribution capable of mimicking the shapes of many distributions and data samples including those with heavy tails. The method of L-moments and the recently developed method of trimmed L-moments (TL-moments) are attractive techniques for parameter estimation for heavy-tailed distributions for which the L- and TL-moments have been defined. Analytical solutions for the first five L- and TL-moments in terms of GLD parameters are derived. Unfortunately, numerical methods are needed to compute the parameters from the L- or TL-moments. Algorithms are suggested for parameter estimation. Application of the GLD using both L- and TL-moment parameter estimates from example data is demonstrated, and comparison of the L-moment fit of the 4-parameter kappa distribution is made. A small simulation study of the 98th percentile (far-right tail) is conducted for a heavy-tail GLD with high-outlier contamination. The simulations show, with respect to estimation of the 98th-percent quantile, that TL-moments are less biased (more robost) in the presence of high-outlier contamination. However, the robustness comes at the expense of considerably more sampling variability. ?? 2006 Elsevier B.V. All rights reserved.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title L-moments and TL-moments of the generalized lambda distribution
Series title Computational Statistics and Data Analysis
DOI 10.1016/j.csda.2006.07.016
Volume 51
Issue 9
Year Published 2007
Language English
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Computational Statistics and Data Analysis
First page 4484
Last page 4496
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