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Trimmed L-moments

Elamir, Elsayed A.H.; Seheult, Allan H.


Elsayed A.H. Elamir

Allan H. Seheult


Classical estimation methods (least squares, the method of moments and maximum likelihood) work well in regular cases such as the exponential family, but outliers can have undue influence on these methods. We define population trimmed L-moments (TL-moments) and corresponding sample TL-moments as robust generalisations of population and sample L-moments. TL-moments assign zero weight to extreme observations, they are easy to compute, their sample variances and covariances can be obtained in closed form, and they are more robust than L-moments are to the presence of outliers. Moreover, a population TL-moment may be well defined where the corresponding population L-moment does not exist: for example, the first population TL-moment is well defined for a Cauchy distribution, but the first population L-moment, the population mean, does not exist. The sample TL-mean is compared with other robust estimators of location.


Elamir, E. A., & Seheult, A. H. (2003). Trimmed L-moments. Computational Statistics & Data Analysis, 43(3), 299-314.

Journal Article Type Article
Publication Date Jul 28, 2003
Deposit Date Feb 29, 2008
Journal Computational Statistics & Data Analysis
Print ISSN 0167-9473
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 43
Issue 3
Pages 299-314
Keywords L-moments, Order statistics, Outliers, Robust estimation, Trimmed mean.

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