Related papers: From subexponential distributions to black swan do…
We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal with "plus" and/or "max"…
Explaining empirically observed wealth and income distributions, featuring power-law tails alongside gamma or log-normal bulk shapes, challenges models that focus on either pairwise competition or individual investment mechanisms. This…
We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi exponential tails, whose coupling coefficients decrease at a subexponential rate. We show that the rates in the strong…
We discuss non-Gaussian random matrices whose elements are random variables with heavy-tailed probability distributions. In probability theory heavy tails of the distributions describe rare but violent events which usually have dominant…
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One…
Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…
Two old conjectures from problem sections, one of which from SIAM Review, concern the question of finding distributions that maximize P(Sn <= t), where Sn is the sum of i.i.d. random variables X1, ..., Xn on the interval [0,1], satisfying…
We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over Aug 1998 - Oct 2004. Specifically, we examine the distributions of (un)directed…
We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean. This type of problems manifests itself when a random variable Y has a…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights…
Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative…
We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main…
We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
We show the equivalence of three properties for an infinitely divisible distribution: the subexponentiality of the density, the subexponentiality of the density of its L\'evy measure and the tail equivalence between the density and its…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…