Related papers: Where Do Thin Tails Come From?
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…
We consider sums of $n$ i.i.d. random variables with tails close to $\exp\{-x^\beta\}$ for some $\beta>1$. Asymptotics developed by Rootz\'en (1987) and Balkema, Kl\"uppelberg & Resnick (1993) are discussed from the point of view of tails…
Let $X_{1},\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics $X_{1:n}\leq \cdots \leq X_{n:n}$ of…
We investigate the behavior of the length of the longest weakly increasing subsequences (weak LIS) of $n$-step random walks with nonzero integer increments $k = \pm 1, \pm 2, \dots$ given by a zero-mean, symmetric heavy tailed mass…
As the data scale grows, deep recognition models often suffer from long-tailed data distributions due to the heavy imbalanced sample number across categories. Indeed, real-world data usually exhibit some similarity relation among different…
A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows asymmetry of scale and also of tail power, whilst avoiding the discontinuity of the second derivative of the split-t (AST) distribution. With…
In this paper, asymptotic behavior of convolution of distributions belonging to two subclasses of distributions with exponential tails are considered, respectively. The precise second-order tail asymptotics of the convolutions are derived…
We consider the tail distribution of the edge cover time of a specific non-Markov process, $\delta$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights…
The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…
In univariate data, there exist standard procedures for identifying dominating features that produce the largest observations. However, in the multivariate setting, the situation is quite different. This paper aims to provide tools and…
Taylors Law (TL) describes the scaling relationship between the mean and variance of populations as a power-law. TL is widely observed in ecological systems across space and time with exponents varying largely between 1 and 2. Many…
We present the results of detailed N-body simulations of clusters moving in a realistic Milky Way (MW) potential. The strong interaction with the bulge and the disk of the Galaxy leads to the formation of tidal tails, emanating from…
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…
Random walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first return time distribution of a 1D random walker, which is a heavy-tailed distribution with infinite…
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…
We present a phenomenological description of the properties of tidal tails forming around dwarf galaxies orbiting the Milky Way. For this purpose we use collisionless N-body simulations of dwarfs initially composed of a disk embedded in an…
Exponential, and not Gaussian, decay of probability density functions was studied by Laplace in the context of his analysis of errors. Such Laplace propagators for the diffusive motion of single particles in disordered media were recently…
Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks etc., these fits usually fail at the tails. Some distributions…
Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also…
We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…