Related papers: Tails of weakly dependent random vectors
The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this…
The class of index-mixed copulas is introduced and its properties are investigated. Index-mixed copulas are constructed from given base copulas and a random index vector, and show a rather remarkable degree of analytical tractability. The…
We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
We propose a simple way of testing whether a given set of observations can come from a given theoretical cumulative distribution. In the test more weight is attached to the tails of the distribution than in the usual Kolmogorov or Smirnov…
We address the problem of estimating the Weibull tail-coefficient which is the regular variation exponent of the inverse failure rate function. We propose a family of estimators of this coefficient and an associate extreme quantile…
In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing…
The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
The sum of Log-normal variates is encountered in many challenging applications such as in performance analysis of wireless communication systems and in financial engineering. Several approximation methods have been developed in the…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.
The present article studies survival analytic aspects of semiparametric copula dependence models with arbitrary univariate marginals. The underlying survival functions admit a representation via exponent measures which have an…
We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the norms of projections of sums of independent…
Extremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend on the order of the variables. In many cases,…
The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear $k$-correlations of $n>k$ independent random variables.
We model systemic risk using a common factor that accounts for market-wide shocks and a tail dependence factor that accounts for linkages among extreme stock returns. Specifically, our theoretical model allows for firm-specific impacts of…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…