Related papers: Tail universalities in rank distributions as an al…
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,…
A new three-parameter cumulative distribution function defined on $(\alpha,\infty)$, for some $\alpha\geq0$, with asymmetric probability density function and showing exponential decays at its both tails, is introduced. The new distribution…
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…
Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…
Motivated by applications in hydrodynamics and networks of thermostatically-control loads in buildings we study control of linear dynamical systems driven by additive and also multiplicative noise of a general position. Utilizing…
Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of…
Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability $p$, then the…
Over the last two decades, it has been argued that the Lorentz transformation mechanism, which imposes the generalization of Newton's classical mechanics into Einstein's special relativity, implies a generalization, or deformation, of the…
Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers…
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 growth dynamics of complex systems often exhibit statistical regularities involving power-law relationships. For real finite complex systems formed by countable tokens (animals, words) as instances of distinct types (species, dictionary…
The goodness-of-fit test for discrimination of two tail distribution using higher order statistics is proposed. The consistency of proposed test is proved for two different alternatives. We do not assume belonging the corresponding…
We propose a simple way of testing whether a given set of observations can come from a given theoretical cumulative distribution. In the test more weight is attached to the tails of the distribution than in the usual Kolmogorov or Smirnov…
In this paper we prove the existence of the high-energy tails for electron distribution function of the Boltzmann equation for semiconductors, in the stationary and homogeneous regime, in the analytic band approximation and scattering with…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One…
There is convincing evidence showing that the probability distributions of stock returns in mature markets exhibit power-law tails and both the positive and negative tails conform to the inverse cubic law. It supports the possibility that…
The purpose of this paper is to show that the use of heavy-tailed distributions in Financial problems is theoretically baseless and can lead to significant misunderstandings. The reason for this the authors see in an incorrect…