14 research outputs found
Extremal attractors of Liouville copulas
Liouville copulas, which were introduced in McNeil and Neslehova (2010), are
asymmetric generalizations of the ubiquitous Archimedean copula class. They are
the dependence structures of scale mixtures of Dirichlet distributions, also
called Liouville distributions. In this paper, the limiting extreme-value
copulas of Liouville copulas and of their survival counterparts are derived.
The limiting max-stable models, termed here the scaled extremal Dirichlet, are
new and encompass several existing classes of multivariate max-stable
distributions, including the logistic, negative logistic and extremal
Dirichlet. As shown herein, the stable tail dependence function and angular
density of the scaled extremal Dirichlet model have a tractable form, which in
turn leads to a simple de Haan representation. The latter is used to design
efficient algorithms for unconditional simulation based on the work of Dombry,
Engelke and Oesting (2015) and to derive tractable formulas for
maximum-likelihood inference. The scaled extremal Dirichlet model is
illustrated on river flow data of the river Isar in southern Germany.Comment: 30 pages including supplementary material, 6 figure
Un'escursione nell'universo in alta dimensione
Ben installati nel nostro mondo in 3D, ci è difficile immaginare e descrivere un universo in quattro o più dimensioni. Solleviamo il velo esplorando le proprietà del cubo e della sfera in alta dimensione
Clustered Archimax Copulas
When modeling multivariate phenomena, properly capturing the joint extremal
behavior is often one of the many concerns. Archimax copulas appear as
successful candidates in case of asymptotic dependence. In this paper, the
class of Archimax copulas is extended via their stochastic representation to a
clustered construction. These clustered Archimax copulas are characterized by a
partition of the random variables into groups linked by a radial copula; each
cluster is Archimax and therefore defined by its own Archimedean generator and
stable tail dependence function. The proposed extension allows for both
asymptotic dependence and independence between the clusters, a property which
is sought, for example, in applications in environmental sciences and finance.
The model also inherits from the ability of Archimax copulas to capture
dependence between variables at pre-extreme levels. The asymptotic behavior of
the model is established, leading to a rich class of stable tail dependence
functions.Comment: 42 pages, 10 figure
Modelling extreme rain accumulation with an application to the 2011 Lake Champlain flood
A simple strategy is proposed to model total accumulation in non-overlapping clusters
of extreme values from a stationary series of daily precipitation. Assuming that each cluster
contains at least one value above a high threshold, the cluster sum S is expressed as the ratio
S=M/P of the cluster maximum M and a random scaling factor P (0, 1]. The joint distribution
for the pair (M, P) is then specified by coupling marginal distributions for M and P with a copula.
Although the excess distribution of M is well approximated by a generalized Pareto distribution,
it is argued that, conditionally on P<1, a scaled beta distribution may already be sufficiently rich
to capture the behaviour of P . An appropriate copula for the pair (M, P) can also be selected by
standard rank-based techniques.This approach is used to analyse rainfall data from Burlington,
Vermont, and to estimate the return period of the spring 2011 precipitation accumulation which
was a key factor in that year’s devastating flood in the RichelieuValley Basin in Qu´ebec, Canada
Un'escursione nell'universo in alta dimensione
Ben installati nel nostro mondo in 3D, ci è difficile immaginare e descrivere un universo in quattro o più dimensioni. Solleviamo il velo esplorando le proprietà del cubo e della sfera in alta dimensione
On the asymptotic covariance of the multivariate empirical copula process
Genest and Segers (2010) gave conditions under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance than the standard empirical process based on a random sample from the underlying copula. An extension of this result to the multivariate case is provided