Journal ArticleDOI
Statistical Methods for Multivariate Extremes: An Application to Structural Design
Stuart Coles,Jonathan A. Tawn +1 more
TLDR
In this paper, the authors apply univariate extreme value theory to quantify the risk of failure due to extreme levels of some environmental process and demonstrate how these ideas can be exploited as part of the design process.Abstract:
For many structural design problems univariate extreme value theory is applied to quantify the risk of failure due to extreme levels of some environmental process. In practice, many forms of structure fail owing to a combination of various processes at extreme levels. Recent developments in statistical methodology for multivariate extremes enable the modelling of such behaviour. The aim of this paper is to demonstrate how these ideas can be exploited as part of the design processread more
Citations
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OtherDOI
Continuous Multivariate Distributions
TL;DR: In this article, the authors present a concise review of developments on various continuous multivariate distributions and present some basic definitions and notations, and present several important continuous multi-dimensional distributions and their significant properties and characteristics.
Journal ArticleDOI
The t copula and related copulas
TL;DR: The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped tCopula, which allow more heterogeneity in the modelling of dependent observations.
Journal ArticleDOI
Dependence Measures for Extreme Value Analyses
TL;DR: In this paper, an overview of the principal issues of extremal dependence is provided through a unified approach which encompasses both the limiting and independent cases of extreme dependence, and diagnostic measures for dependence are also developed.
Journal ArticleDOI
Statistics for near independence in multivariate extreme values
TL;DR: In this article, a multivariate extreme value threshold model for joint tail estimation is proposed, which overcomes the problems encountered with existing techniques when the variables are near independence, and tests for independence of extremes of the marginal variables, both when the thresholds are fixed and when they increase with the sample size.
Journal ArticleDOI
A conditional approach for multivariate extreme values (with discussion)
TL;DR: In this article, a semiparametric approach is proposed to analyze air pollution data and reveal complex extremal dependence behavior that is consistent with scientific understanding of the process. But it is not suitable for applications where the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the joint distribution where only a subset of components is extreme.
References
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Book
Extreme Values, Regular Variation, and Point Processes
TL;DR: In this paper, the authors present a survey of the main domains of attraction and norming constants in point processes and point processes, and their relationship with multivariate extremity processes.
Book
The asymptotic theory of extreme order statistics
TL;DR: In this article, the authors analyze the recent development of the theory of the asymptotic distribution of extremes in the light of the questions (i) and (ii). Several dependence concepts will be introduced, each of which leads to a solution of (i).
Book
Tides, Surges and Mean Sea-Level
TL;DR: Tidal Patterns Meteorological and Other Non-tidal Disturbances Some Definitions of Common Terms Basic Statistics of Tides as Time Series Observations and Data Reduction Forces Analysis and Prediction Tidal Dynamics Biology: Some Tidal Influences Filters for Tidal Time Series Response Analysis Inputs and Theory Analysis of Currents Theoretical Tidal dynamics Legal Definitions in the Coastal Zone as discussed by the authors.
Journal ArticleDOI
On the theory of elliptically contoured distributions
TL;DR: The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity as mentioned in this paper, where the distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg on spherically symmetric distributions.