Trimmed L-moments

Elamir, Elsayed A. H.; Seheult, Allan

doi:10.1016/s0167-9473(02)00250-5

Cited by 136 publications

(123 citation statements)

References 15 publications

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“…The advantage of this procedure is that it deals with the whole probability model. It is less sensitive for the choice of trimming for each parameter separately [11]. The r th , TL-moments can be written as: Fig.…”

Section: Methodsmentioning

confidence: 99%

“…To accomplish this study, we applied robust estimation methods such as L-moments as introduced by Hosking [10], plus TL-moments introduced by Elamir and Seheult [11] and LH-moments introduced by Wang [12]. These techniques have many advantages over other estimation methods such as moments and maximum likelihood method (e.g., [10][11][12][13][14][15][16][17][18][19][20][21][22]), and many more. L-moments are analogous to conventional moments showing some advantages over conventional moments.…”

Section: Introductionmentioning

confidence: 99%

“…Since 1990, L-moments has been widely used by many researchers across the world in a variety of fi elds [24][25][26][27]. In order to avoid undue favor due to outliers in data, a more robust estimation method (i.e., TL-moments as introduced by Elamir and Seheult [11]) can be used. TL-moments assign zero weight to extreme values in the data and claim to be more robust than simple L-moments in the presence of outliers in the data [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Ahmad

Abbass²,

Saghir

et al. 2016

Pol. J. Environ. Stud.

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In this study, at-site frequency analysis (AFA) of an annual daily maximum rainfall (ADMR) series was carried out using the method of linear moments (L-moments) and their variants such as trimmed linear moments (TL-moments) and higher order linear moments (LH-moments). The ADMR series we investigated was observed at 28 meteorological observatories across Pakistan as retrieved from the Pakistan Meteorological Department (PMD). The basic aim of the study was to fi nd best-fi t (i.e., the most suitable) probability distribution among the class of various probability distributions. Initially different goodness-offi t (GOF) measures such as the Kolmogorov-Smirnov test (KST), Anderson-Darling test (ADT), root mean square error (RMSE) and L-moments ratio diagram (LRD) were applied to determine not only the best-fi t distributions but also the best linear estimation method for AFA. We observed that no single probability distribution could be declared as the best-fi t distribution for all the stations. Five distributions were found to be the most appropriate: generalized extreme value (GEV), three parameter lognormal (LN3), Pearson type III (P3), generalized logistic (GLO), and generalized pareto (GPA). The TL-moments method was also applied for parameter estimation to mitigate the effect of outliers on fi nal estimates. LH-moments were used for estimating the upper part of probability distributions and larger events in the data samples. LH moments alleviate the unwanted affects due to small sample values that may be obvious during estimation of events related to larger return periods. Using different GOF tests, we observed that the L-moments method was best for eight stations, TL-moments with trimming (1, 0), and LH-moments with level η =2, 3, 4 were best for six and 14 stations, respectively. A theoretical relationship between TL-moments and LH-moments was also revisited, which revealed that LH-moments are special cases of TL-moments when we are motivated to make trimming only from the lower side.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Ahmad

Abbass²,

Saghir

et al. 2016

Pol. J. Environ. Stud.

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show abstract

“…Elamir and Seheult (2003) introduced Trimmed Lmoments (TL-moments) as an alternative to LQ-moments and natural generalization of L-moments that do not http://journals.uob.edu.bh require the mean of underlying distribution to exist. TLmoments depend on giving zero weight to extreme observations.…”

Section: Introductionmentioning

confidence: 99%

“…For example, TL-moments give more robust estimators than L-moments in the presence of outliers. Moreover, population TL-moments may be well defined where the corresponding population L-moments (or central moments ) do 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 (see, Elamir and Seheult (2003)). …”

Section: Introductionmentioning

confidence: 99%

Linear Moments: An Overview

Kandeel¹

2015

IJBSA

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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.

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Risk Measures: Statistical Estimation

Gouriéroux

2010

Encyclopedia of Quantitative Finance

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This article presents the main risk measures suggested in the current regulations for finance (Basel 2) and insurance (Solvency 2) to fix the reserves, which are the Value‐at‐Risk (VaR), Tail‐VaR, and the distortion risk measures (DRM). These measures can be used in a conditional or an unconditional framework. We explain how they can be estimated and give the distributional properties of the estimator. Finally, we interpret the selection of reserve levels as a control problem and explain how this interpretation can be used to check the methodologies proposed by banks or insurance companies to the regulators.

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Trimmed L-moments

Cited by 136 publications

References 15 publications

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Linear Moments: An Overview

Risk Measures: Statistical Estimation

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