Related papers: Insights into Tail-Based and Order Statistics

In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…

The statistical distribution of the ratio of two normal random variables is characterized by its heavy-tailed nature and absence of finite moments. The shape of its density function is highly variable, capable of exhibiting unimodal or…

The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…

We consider the fitting of heavy tailed data and distribution with a special attention to distributions with a non--standard shape in the "body" of the distribution. To this end we consider a dense class of heavy tailed distributions…

This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…

Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…

We investigate the relation between moments and tails of heavy-tailed (in particular, Pareto-type) distributions. We also discuss the sharpness of our results in a number of examples under certain regularity conditions like log-convexity.…

We propose a new measure related with tail dependence in terms of correlation: quantile correlation coefficient of random variables X, Y. The quantile correlation is defined by the geometric mean of two quantile regression slopes of X on Y…

We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…

This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…

Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric,…

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each…

In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…

Human activities can play a crucial role in the statistical properties of observables in many complex systems such as social, technological and economic systems. We demonstrate this by looking into the heavy-tailed distributions of…

This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case.…

This paper proposes a new method to combine several densities such that each density dominates a separate part of a joint distribution. The method is fully unsupervised, i.e. the parameters in the densities and the thresholds are…

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…

We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…