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314309

The Influence Functions and Breakdown Points of the L-Moments, Tl-Moments and the LQ-Moments Estimators

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Last updated: 05 Jan 2025

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Abstract

The L-moments are defined as linear combinations of expected values of order statistics of an absolutely continuous random variable, (Hosking 1990). The advantages of L- moments over classical moments are: able to characterize a wider range of distributions; and the L-moments estimators are "more robust to the presence of outliers". Elamir and Seheult (2003) introduced an extension of L-moments called TL-moments. TL-moments estimators are assumed to be "more robust against outliers" than L-moments estimators. Mudholkar and Hutson (1998) introduced LQ-moments estimators as a "robust" version of the I- moments estimators. It is essential to study robustness of the above estimators according to the basic criteria to assess robustness. Namely, an estimator is locally robust if its influence function is bounded with small gross-error sensitivity. An estimator is globally robust if its breakdown point is large. In this paper we derive the influence function and the breakdown point for the L-moments, the LQ-moments and the TL-moments estimators.

DOI

10.21608/esju.2011.314309

Keywords

L-Moments - Tl-Moments - Ql-Moments - Influence Function - Gross Error, Sensitivity - Breakdown Poin

Volume

55

Article Issue

1

Related Issue

43106

Issue Date

2011-06-01

Publish Date

2011-06-01

Page Start

22

Page End

39

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_314309.html

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https://esju.journals.ekb.eg/service?article_code=314309

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3

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Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

The Influence Functions and Breakdown Points of the L-Moments, Tl-Moments and the LQ-Moments Estimators

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Type

Article

Created At

28 Dec 2024