L-moments and TL-moments of the generalized lambda distribution
Computational Statistics and Data Analysis
By: W.H. Asquith
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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.
Suggested Citation
Asquith, W., 2007, L-moments and TL-moments of the generalized lambda distribution: Computational Statistics and Data Analysis, v. 51, no. 9, p. 4484-4496, https://doi.org/10.1016/j.csda.2006.07.016.
| 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 |