Robust and Computationally Efficient Trimmed L-Moments Estimation for Parametric Distributions

Chudamani Poudyal; Qian Zhao; Hari Sitaula

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arXiv · 2505.09860

Robust and Computationally Efficient Trimmed L-Moments Estimation for Parametric Distributions

Chudamani Poudyal·Qian Zhao·Hari Sitaula

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Abstract

This paper proposes a robust and computationally efficient estimation framework for fitting parametric distributions based on trimmed L-moments. Trimmed L-moments extend classical L-moment theory by downweighting or excluding extreme order statistics, resulting in estimators that are less sensitive to outliers and heavy tails. We construct estimators for both location-scale and shape parameters using asymmetric trimming schemes tailored to different moments, and establish their asymptotic properties for inferential justification using the general structural theory of L-statistics, deriving simplified single-integration expressions to ensure numerical stability. State-of-the-art algorithms are developed to resolve the sign ambiguity in estimating the scale parameter for location-scale models and the tail index for the Frechet model. The proposed estimators offer improved efficiency over traditional robust alternatives for selected asymmetric trimming configurations, while retaining closed-form expressions for a wide range of common distributions, facilitating fast and stable computation. Simulation studies demonstrate strong finite-sample performance. An application to financial claim severity modeling highlights the practical relevance and flexibility of the approach.

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Chudamani Poudyal, Qian Zhao, Hari Sitaula. 2025-05-14. Robust and Computationally Efficient Trimmed L-Moments Estimation for Parametric Distributions. https://arxiv.org/abs/2505.09860

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