Related papers: Heavy-Tail Distribution from Correlation of Discre…
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…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
We study a stochastic process defined by the interaction strength for the return to the mean and a stochastic term proportional to the magnitude of the variable. Its steady-state distribution is the Inverse Gamma distribution, whose…
We present a simple model of a stock market where a random communication structure between agents gives rise to a heavy tails in the distribution of stock price variations in the form of an exponentially truncated power-law, similar to…
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…
We study the tails of closing auction return distributions for a sample of liquid European stocks. We use the stochastic call auction model of Derksen et al. (2020a), to derive a relation between tail exponents of limit order placement…
Various molecular interaction networks have been claimed to follow power-law decay for their global connectivity distribution. It has been proposed that there may be underlying generative models that explain this heavy-tailed behavior by…
A particular direction of recent advance about stochastic deep-learning algorithms has been about uncovering a rather mysterious heavy-tailed nature of the stationary distribution of these algorithms, even when the data distribution is not…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…
We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…
A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being transient. These distributions are mathematically tractable…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
Recently, increasing empirical evidence indicates the extensive existence of heavy tails in the interevent time distributions of various human behaviors. Based on the queuing theory, the Barab\'asi model and its variations suggest the…
Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…
Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is…
Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…
It is well known that the distribution of returns from various financial instruments are leptokurtic, meaning that the distributions have "fatter tails" than a Normal distribution, and have skew toward zero. This paper presents a graceful…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…