Exact variance structure of sample L-moments

Elamir, Elsayed A. H.; Seheult, Allan

doi:10.1016/s0378-3758(03)00213-1

Cited by 34 publications

(25 citation statements)

References 18 publications

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“…Elamir and Seheult (2004) derive the exact variance structure of sample L-moments in the non-asymptotic case without formulating assumptions on the underlying parent distributions. Let's call the variances and covariances of the sample Probability Weighted Moments θ kk = var(b k ) and θ kl = cov(b k ,b l ), respectively.…”

Section: Variance Of the Sample L-cvmentioning

confidence: 99%

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Confidence intervals for the coefficient of L-variation in hydrological applications

Viglione

2010

Hydrol. Earth Syst. Sci.

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Abstract. The coefficient of L-variation (L-CV) is commonly used in statistical hydrology, in particular in regional frequency analysis, as a measure of steepness for the frequency curve of the hydrological variable of interest. As opposed to the point estimation of the L-CV, in this work we are interested in the estimation of the interval of values (confidence interval) in which the L-CV is included at a given level of probability (confidence level). Several candidate distributions are compared in terms of their suitability to provide valid estimators of confidence intervals for the population L-CV. Monte-Carlo simulations of synthetic samples from distributions frequently used in hydrology are used as a basis for the comparison. The best estimator proves to be provided by the log-Student t distribution whose parameters are estimated without any assumption on the underlying parent distribution of the hydrological variable of interest. This estimator is shown to also outperform the non parametric bias-corrected and accelerated bootstrap method. An illustrative example of how this result can be used in hydrology is presented, namely in the comparison of methods for regional flood frequency analysis. In particular, it is shown that the confidence intervals for the L-CV can be used to assess the amount of spatial heterogeneity of flood data not explained by regionalization models.

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Section: Variance Of the Sample L-cvmentioning

confidence: 99%

“…To meet this aim, we exploit the results of a distribution-free approach, recently proposed by the statistical community, to derive estimators for variances and covariances of sample L-moments (Elamir and Seheult, 2004). The estimators of the sample L-CV and its variance are used to fit several two-parameters candidate sampling distributions (Sect.…”

mentioning

confidence: 99%

Confidence intervals for the coefficient of L-variation in hydrological applications

Viglione

2010

Hydrol. Earth Syst. Sci.

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“…The L-moments of samples are defined in figure 3-2, which provides definitions for whole samples and for a type of censored data germane to this study (Wang and others, 2010). The variance-covariance structure of the sample L-moments used for this study is defined in figure 3-3 following the definitions of Elamir and Seheult (2004) and implementations by and . Lastly, the sample variancecovariance computations are dependent on probabilityweighted moments (PWMs, defined in fig.…”

Section: Appendix 1 References Citedmentioning

confidence: 99%

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

Asquith¹,

Kiang²,

Cohn³

2017

Scientific Investigations Report

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“…To evaluate the exact variance of sample EM we note that sample EM is linear combinations of order statistics and their particular form allows us to use the method of Elamir and Seheult (2004) and Downton (1966) to obtain the exact variances in terms of expectations, variances and covariances of order statistics from samples of fixed size which do not depend on the actual sample size as 14…”

Section: Exact Variance Of Sample Extended Meanmentioning

confidence: 99%

Extended Mean with Distribution-Free Variance

Kandil¹,

Hamza²

2015

IJBSA

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Location estimation is one of the basic activities in statistical data analysis so considerable effort has been put into the development of procedures for the robust estimation of measures of location. Because the distribution-free variance of most of existing measures is difficult to obtain in closed form, these measures work under strong modelling assumptions. We propose a robust location measure in which the expectation of a lower order statistics is replaced by the expectation of a larger order statistics. The main attraction of this measure is that its distribution-free variance is obtained in closed form. Comparisons with some of the best location estimators, mean, Hodges-Lehmann estimator, Huber's M-estimator and median are given based on Monte Carlo simulations. Computationally, the new estimator has an explicit expression and requires no iteration.

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Exact variance structure of sample L-moments

Cited by 34 publications

References 18 publications

Confidence intervals for the coefficient of L-variation in hydrological applications

Confidence intervals for the coefficient of L-variation in hydrological applications

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

Extended Mean with Distribution-Free Variance

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