Related papers: Location- and scale-free procedures for distinguis…

In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…

We discuss in this paper a possibility of constructing a whole class of asymptotic distribution-free tests for testing regularly varying tail distributions. The idea is that we treat the tails of distributions as members of a parametric…

We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the…

Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…

The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, 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…

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…

This paper introduces a class of copula models for spatial data, based on multivariate Pareto-mixture distributions. We explore the tail properties of these models, demonstrating their ability to capture both tail dependence and asymptotic…

Geographical phenomena fall into two categories: scaleful phenomena and scale-free phenomena. The former bears characteristic scales, and the latter has no characteristic scale. The conventional quantitative and mathematical methods can…

Heavy tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with Internet transaction datasets, and machine learners often analyze such data without considering the biases…

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…

In the real world, long-tailed data distributions are prevalent, making it challenging for models to effectively learn and classify tail classes. However, we discover that in the field of drug chemistry, certain tail classes exhibit higher…

Both empirical and theoretical investigations of scale-free network models have found that large degrees in a network exert an outsized impact on its structure. However, the tools used to infer the tail behavior of degree distributions in…

The normal distribution and its perturbation has left an immense mark on the statistical literature. Hence, several generalized forms were developed to model different skewness, kurtosis, and body shapes. However, it is not easy to…

Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes…

We propose the test for distinguishing between two classes of distribution tails using only the largest order statistics of the sample and state its consistency. We do not assume belonging the corresponding distribution functions to any…

How to estimate the uncertainty of a given model is a crucial problem. Current calibration techniques treat different classes equally and thus implicitly assume that the distribution of training data is balanced, but ignore the fact that…

Real-world data are long-tailed, the lack of tail samples leads to a significant limitation in the generalization ability of the model. Although numerous approaches of class re-balancing perform well for moderate class imbalance problems,…

In the study of heavy tail data, several models have been introduced. If the interest is in the tail of the distribution, block maxima or excess over thresholds are the typical approaches, wasting relevant information in the bulk of the…

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…