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Zbl 1162.62312
Asquith, William H.
L-moments and TL-moments of the generalized lambda distribution. (English)
[J] Comput. Stat. Data Anal. 51, No. 9, 4484-4496 (2007). ISSN 0167-9473

Summary: 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 98\,th percentile (far-right tail) is conducted for a heavy-tail GLD with high-outlier contamination. The simulations show, with respect to estimation of the 98\,th-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.

MSC 2000:: *62E15 Exact distribution theory in statistics
65C60 Computational problems in statistics

Keywords: L-moments; TL-moments; order statistics; generalized lambda distribution; robust estimation

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Zentralblatt MATH Berlin [Germany]