Related papers: On Goodhart's law, with an application to value al…

In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…

To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…

This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large…

We introduce a new stochastic order for the tail dependence between random variables. We then study different measures of tail dependence which are monotone in the proposed order, thereby extending various known tail dependence coefficients…

Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…

It is not uncommon that real-world data are distributed with a long tail. For such data, the learning of deep neural networks becomes challenging because it is hard to classify tail classes correctly. In the literature, several existing…

We investigate the ordering between two fundamental measures of dispersion for real-valued risks: the standard deviation (SD) and the Gini mean difference (GMD). Our analysis is driven by a single structural object, namely the mean excess…

We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…

The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

Many data distributions in the real world are hardly uniform. Instead, skewed and long-tailed distributions of various kinds are commonly observed. This poses an interesting problem for machine learning, where most algorithms assume or work…

A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively…

Due to the skessed distribution, high peak and thick tail and asymmetry of financial return data, it is difficult to describe the traditional distribution. In recent years, generalized autoregressive score (GAS) has been used in many fields…

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…

We consider a family of distributions on which natural tail orders can be constructed upon a representation of a distribution by a (single) hyper-real number. Past research revealed that the ordering can herein strongly depend on the…

We propose a new heavy-tailed distribution --- Gaussian-Chain (GC) distribution, which is inspirited by the hierarchical structures prevailing in social organizations. We determine the mean, variance and kurtosis of the Gaussian-Chain…

The size of the giant component in the configuration model, measured by the asymptotic fraction of vertices in the component, is given by a well-known expression involving the generating function of the degree distribution. In this note, we…

Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, hierarchical models for collective risk with heavy-tails of the claims distributions that take also…

This study introduces a new analytical framework for quantifying multivariate risk measures. Using the Wishart process, which is a stochastic process with values in the space of positive definite matrices, we derive several conditional tail…