Corpus ID: 14879753


  author={Richard L. Smith},
Max-stable processes arise from an infinite-dimensional generalisation of extreme value theory. They form a natural class of processes when sample maxima are observed at each site of a spatial process, a problem of particular interest in connection with regional estimation methods in hydrology. A general representation of max-stable processes due to de Haan and Vatan is discussed, and examples are given to show how it may be used to generate explicit examples of max-stable process. As a side… Expand
Max-stable Processes for Threshold Exceedances in Spatial Extremes
Max-stable Processes for Threshold Exceedances in Spatial Extremes (Under the direction of Richard L. Smith) The analysis of spatial extremes requires the joint modeling of a spatial process at aExpand
1 Spatial Extremes and max-stable processes
This chapter aims at being a crash course on max-stable processes with an emphasis on their use for modeling spatial extremes. We will see how maxstable processes are defined through a simpleExpand
Dependence Structure of Spatial Extremes Using Threshold Approach
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processesExpand
Non-Stationary Dependence Structures for Spatial Extremes
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, severalExpand
A flexible dependence model for spatial extremes
Abstract Max-stable processes play a fundamental role in modeling the spatial dependence of extremes because they appear as a natural extension of multivariate extreme value distributions. InExpand
A finite-dimensional construction of a max-stable process for spatial extremes
From heat waves to hurricanes, often the environmental processes that are the most critical to understand probabilistically are extreme events. Such extremal processes manifestly exhibit spatialExpand
Max-stable processes for modelling extremes observed in space and time
Abstract Max-stable processes have proved to be useful for the statistical modeling of spatial extremes. For statistical inference it is often assumed that there is no temporal dependence; i.e., thatExpand
On Some Environmental Applications of Stochastic Processes
This dissertation focuses on the study of some environmental applications of stochastic processes. In the first Chapter, we study an extreme value time series, where the extremes are derived usingExpand
Conditioned limit laws for inverted max-stable processes
This work studies broad classes of inverted max-stable processes containing processes linked to the widely studiedmax-stable models of Brown-Resnick and extremal- t and identifies conditions for the normalisations to either belong to the canonical family or not. Expand
Conditional simulations of the extremal t process: application
  • L. Bel
  • Mathematics, Computer Science
  • 2014
In this work conditional simulations are investigated for the extremal t process taking benets of its spectral construction taking into account the role of the dierent parameters of the model and the importance of the steps of the algorithm. Expand


Bivariate extreme-value data and the station-year method
Abstract The theory of bivariate extremes is concerned with the joint distribution of maxima at two different sites. In hydrology, this theory is important when one wishes to apply the station-yearExpand
Modelling multivariate extreme value distributions
SUMMARY Multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima/minima. No parametric family exists for the depen- dence between theExpand
Bivariate extreme value theory: Models and estimation
SUMMARY Bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima. No natural parametric family exists for the dependence between the marginalExpand
Estimating a regional flood frequency distribution
When floods at different sites are assumed to arise from the same distribution except for scale (U.S. Geological Survey's Index Flood Method), one can attempt to identify the dimensionless flood-flowExpand
Models for exceedances over high thresholds
We discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds. The natural distribution for such exceedances, the generalized ParetoExpand
Extremes and local dependence in stationary sequences
SummaryExtensions of classical extreme value theory to apply to stationary sequences generally make use of two types of dependence restriction:(a)a weak “mixing condition” restricting long rangeExpand
The effect of intersite dependence on regional flood frequency analysis
Regional flood frequency analysis usually assumes that flood records from different sites are statistically independent. This assumption is unlikely to be valid in practice, so it is important toExpand
Stationary min-stable stochastic processes
We consider the class of stationary stochastic processes whose margins are jointly min-stable. We show how the scalar elements can be generated by a single realization of a standard homogeneousExpand
A simple spatial-temporal model of rainfall
  • D. Cox, V. Isham
  • Geography
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1988
A spatial-temporal model of rainfall is studied in which storms arrive in a Poisson process in space and time, each storm consisting of a circular region of rain which moves with random velocity forExpand
Estimating probabilities of extreme sea-levels
A key problem in the design of sea defences is the estimation of quantiles of the distribution of annual maximum hourly sea‐levels. Traditional statistical analyses fail to exploit the considerableExpand