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

Computational Statistics and Data Analysis

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DOI: 10.1016/j.csda.2006.07.016

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Abstract

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
Number of Pages:
13