An Introduction to Statistical Modeling of Extreme Values

By Eric P. Smith. Technometrics, 2002

1,064 citations recorded by the source corpus.

Subfields: Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/57e676cad3491d9d2e04f2a02f2413e325c5ff70

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In Management Science and Operations Research

Citations in the corpus

The European climate under a 2 °C global warming (2014, methodology): “Return values are estimated using the block maxima method for which the generalized extreme value (GEV) distribution describes the behavior of said maxima (Coles 2001). The approach closely follows that of Nikulin et al (2011) and further details are provided therein.”
Assessment methods for unsteady flow distortion in aero-engine intakes (2018, methodology): “[12] first proposed to use Extreme Value Theory (EVT) [24] to predict the maximum level of a given distortion metric to be expected after a given operating time with well-defined confidence intervals.”
Characteristics of unsteady total pressure distortion for a complex aero-engine intake duct (2018, positive): “From the estimated model parameters, the m-observation return level value 𝑥 𝑚 is obtained with (Eq.15) [18].”
ESTIMATION OF TAIL RISK MEASURES IN FINANCE: APPROACHES TO EXTREME VALUE MIXTURE MODELING (2019, background): “According to Coles(2001), the modified scale parameter is 𝜎𝑢 − 𝑢𝜉.”
A Bayesian Hierarchical Approach to Multivariate Nonstationary Hydrologic Frequency Analysis (2018, background): “A number of probability distributions are available to describe the behavior of extremes, including the generalized extreme value (GEV) distribution and the generalized pareto distribution (GPD), both of which are consistent with extreme value theory (EVT; Coles, 2001).”
A unified statistical model for hydrological variables including the selection of threshold for the peak over threshold method (2012, methodology): “The first framework is the most widely adopted [Coles, 2001] and includes the POT method. In contrast, the second framework may require the use of more sophisticated statistical models and will not be discussed here. [12] The POT method is considered to be the declustering method most commonly used ”
Statistical analysis on extreme wave height (2012, background): “This also has been proven in a theoretical way by Langbein (1947) and Chow et al. (1988).”
Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality (2018, background): “Under very reasonable assumptions, the tails of continuous probability distributions converge to the Generalized Pareto Distribution (GPD), a form of powerlaw distribution (Coles et al., 2001).”
Evaluation and future projections of temperature, precipitation and wind extremes over Europe in an ensemble of regional climate simulations (2011, methodology): “Unfortunately, as we have already mentioned in the introduction, there is no suitable observational database to evaluate the simulated Wmax,20.”
Spatiotemporal wildfire modeling through point processes with moderate and extreme marks (2021, background): “Given a random variable X whose distribution F satisfies mild regularity conditions, the generalized Pareto distribution (GPD) arises asymptotically for the positive excesses of X above a threshold increasing to x⋆ = sup{x : F (x) 1} (Coles, 2001).”
Dimensionality-Driven Learning with Noisy Labels (2018, background): “From the statistical theory of extreme values, the tails of continuous distance distributions can be seen to converge to the Generalized Pareto Distribution (GPD), a form of power-law distribution (Coles et al., 2001; Hill, 1975).”
A two-step framework for over-threshold modelling of environmental extremes (2014, positive): “…approach widely spread in extreme value analyses, together with the application of the GPD, (Davison and Smith, 1990; Simiu and Heckert, 1995; Embrechts et al., 1997; Palutikof et al., 1999; Coles, 2001; Mackay et al., 2001; Pandey et al., 2001; Rosbjerg and Madsen, 2004; Ribatet et al., 2007).”
Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction (2012, methodology): “plus-minus three standard errors as derived from the profile likelihood (Coles, 2001).”
Evaluation of classical spatial-analysis schemes of extreme rainfall (2012, methodology): “These approaches are based on the generalized extreme-value (GEV) distribution (Coles (2001), Sect.”
Statistical mechanics of complex neural systems and high dimensional data (2013, background): “Indeed, the Gumbel distribution is a universal distribution governing extreme values of any random variables whose tails vanish faster than exponentially [116]; this strong suppression of extreme values in any single variable directly leads to an extremely slow √ lnR growth of the maximum over R rea”
Ultra-Reliable Low-Latency Vehicular Networks: Taming the Age of Information Tail (2018, methodology): “First, we need to introduce the Pickands–Balkema–de Haan theorem for exceedances over threshold [6].”