Linear Moments: An Overview

Abstract

Many statistical techniques are based on the use of linear combinations of order statistics that called linear moments. L-moments are a sequence of statistics used to summarize the shape of a probability distribution. They are linear combinations of order statistics analogous to conventional moments, and can be used to calculate quantities analogous to standard deviation, skewness and kurtosis, termed the L-scale, L-skewness and L-kurtosis respectively. In this paper an overview for recent works in Lmoments is presented.

Application of at-site peak-streamflow frequency analyses for very low annual exceedance probabilities

“…The core mathematics of L-moments shown in this appendix are thoroughly reviewed by , , Kandeel (2015), Stedinger and others (1993), and Nair and Vineshkumar (2010), and extensions available in Asquith (2011a,b), , and Seheult (2003, 2004). In particular, the mathematics herein are listed in near verbatim from typesetting sources of Asquith (2011a,b) and .…”

An inovative regional frequency analysis approach for robust extreme precipitation assessment in data-rich and climatically diverse regions

“…L-moment analysis differs from typical moment-based methods by utilising linear combinations of order statistics, known as L-moments, which serve as reliable estimators of population moments (Sahu et al 2021). Lmoments offer valuable insights into the morphology, spatial distribution, and magnitude of a distribution, rendering them valuable for the purpose of fitting probability distributions to empirical data, estimating parameters, and drawing conclusions regarding exceptional occurrences (Kandeel 2015). This methodology is especially advantageous when addressing distributions that are skewed or heavy-tailed, which are frequently observed in hydrological and environmental datasets (Nerantzaki and Papalexiou 2022).…”