A Moment Estimator for the Index of an Extreme-Value Distribution

Dekkers, Arnold; Einmahl, J.H.J.; Haan, Leo de

doi:10.1214/aos/1176347397

Cited by 567 publications

(371 citation statements)

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“…Lechner et al (1993) use simulated wind speed data to compare three methods for estimating the GPD parameters: conditional mean exceedance (CME), Pickands (Pickands, 1975) and Dekkers-Einmahl-de Haan (DED), which provides a moment-based estimator (Dekkers et al, 1989). They obtain good results for the CME and DED methods and, for wind engineering applications, recommend the DED approach.…”

Section: Selection Of Methods For Parameter Estimationmentioning

confidence: 99%

A review of methods to calculate extreme wind speeds

Palutikof

Brabson

Lister

et al. 1999

Meteorological Applications

322

209

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High wind speeds pose a threat to the integrity of structures, particularly those at exposed sites such as bridges, wind turbines and radio masts. In any design project for large structures, safety considerations must be balanced against the additional cost of 'over-design'. Accurate estimation of the occurrence of extreme wind speeds is an important factor in achieving the correct balance. Such estimates are commonly expressed in terms of the quantile value X T , i.e., the maximum wind speed which is exceeded, on average, once every T years, the return period. Typically, for most users of wind data, estimates of the 50-year return period gust or wind speed are required, based on 10-20 (and often fewer) available years of observations. For this situation, the data are generally fitted to a theoretical distribution in order to calculate the quantiles. Fisher & Tippett (1928) showed that if a sample of n cases is chosen from a parent distribution, and the maximum (or minimum) of each sample is selected, then the distribution of the maxima (or minima) approaches one of three limiting forms as the size of the samples increases. Gumbel (1958) argued that, in the case of floods, each year of record constitutes a sample with 365 cases and that the annual extreme flood is the maximum value of the sample. Thus, the Fisher-Tippett distributions could be fitted to the set of annual maxima. This is the basis of all classical extreme value theory. The aim is to define the form of the limiting distribution and estimate the parameters, so that values of X T can be calculated.Here, we review and summarize the portion of the extensive literature on extreme value theory relevant to the analysis of wind and gust speed data. The review is carried out with reference to the requirements of a user seeking to select and apply a method appropriate to a particular real data set. We discuss first the available techniques and then the choices required for successful selection and implementation. The methods are organized broadly according to the length of the time series of observations available for analysis, beginning with those which require longer data sets, and moving towards those developed for use with short-duration series. The length of the observational data set is often a problem for those wishing to calculate extreme wind speed quantiles but is a common concern for users of geophysical data, and a substantial literature exists on estimation of extremes from short time series.Note that we do not consider here the matter of anemometer exposure. As with all analyses of wind data, the results of an extreme value analysis will be flawed if the data on which they are based are taken from an anemometer with a non-standard exposure (e.g., sheltered in one or more directions, or at a height above the ground different from the 10 m standard).Meteorol. Appl. 6, 119-132 (1999) A review of methods to calculate extreme wind speeds

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Section: Selection Of Methods For Parameter Estimationmentioning

confidence: 99%

A review of methods to calculate extreme wind speeds

Palutikof

Brabson

Lister

et al. 1999

Meteorological Applications

322

209

View full text Add to dashboard Cite

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“…Hill (1975), Pickands (1975), Csörgő et al (1985), Dekkers et al (1989)). Here we consider the following estimator for γ > 0, the geometric-type (GT) estimator…”

Section: Extreme Value Theorymentioning

confidence: 99%

“…The asymptotic behavior of these quantile estimators was studied and their asymptotic normality was proved (cf. Brito et al (2014), Dekkers et al (1989) and de Haan and Rootzén (1993)). …”

Section: Extreme Value Theorymentioning

confidence: 99%

Modeling of Extremal Earthquakes

Brito

Cavalcante

Freitas

2015

CIM Series in Mathematical Sciences

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Natural hazards, such as big earthquakes, affect the lives of thousands of people at all levels. Extreme-value analysis is an area of statistical analysis particularly concerned with the systematic study of extremes, providing an useful insight to fields where extreme values are probable to occur. The characterization of the extreme seismic activity is a fundamental basis for risk investigation and safety evaluation. Here we study large earthquakes in the scope of the Extreme Value Theory. We focus on the tails of the seismic moment distributions and we propose to estimate relevant parameters, like the tail index and high order quantiles using the geometric-type estimators.In this work we combine two approaches, namely an exploratory oriented analysis and an inferential study. The validity of the assumptions required are verified, and both geometric-type and Hill estimators are applied for the tail index and quantile estimation. A comparison between the estimators is performed, and their application to the considered problem is illustrated and discussed in the corresponding context.

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“…Univariate simulation and distribution functions are implemented, as is estimation of stationary models for the GEV and GPD using maximum likelihood and probability weighted moments. The quantile based financial measure known as value-at-risk can be calculated explicitly, and plots of tail index estimates can be produced using the estimators of Hill (1975), Pickands (1975) and Dekkers et al (1989).…”

Section: R Software Packagesmentioning

confidence: 99%

A software review for extreme value analysis

2012

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Extreme value methodology is being increasingly used by practitioners from a wide range of fields. The importance of accurately modeling extreme events has intensified, particularly in environmental science where such events can be seen as a barometer for climate change. These analyses require tools that must be simple to use, but must also implement complex statistical models and produce resulting inferences. This document presents a review of the software that is currently available to scientists for the statistical modeling of extreme events. We discuss all software known to the authors, both proprietary and open source, targeting different data types and application areas. It is our intention that this article will simplify the process of understanding the available software, and will help promote the methodology to an expansive set of scientific disciplines.

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A Moment Estimator for the Index of an Extreme-Value Distribution

Cited by 567 publications

References 0 publications

A review of methods to calculate extreme wind speeds

A review of methods to calculate extreme wind speeds

Modeling of Extremal Earthquakes

A software review for extreme value analysis

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