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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…
We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. We show the subword complexity and the growth function create machine invariant classes. So the…
In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
We consider the polarization of Lambda + Lambda-bar baryons produced in polarized Deep Inelastic Scattering at leading order, with various spin configurations: longitudinally polarized leptons and unpolarized nucleon; unpolarized leptons…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice in the critical region are investigated. We study numerically two scaling functions:…
Employing the framework of regular variation, we propose two decompositions which help to summarize and describel high-dimensional tail dependence. Via transformation, we define a vector space on the positive orthant, yielding the notion of…
In this paper, we will give a sufficient condition for a non-negative random variable $X$ to be heavy tailed by investigating the Laplace-Stieltjes transform of the probability distribution function. We focus on the relation between the…
In this paper, we introduce reduced-bias estimators for the estimation of the tail index of a Pareto-type distribution. This is achieved through the use of a regularised weighted least squares with an exponential regression model for…
We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…
The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
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…
We study stochastic dominance between portfolios of independent and identically distributed (iid) extremely heavy-tailed (i.e., infinite-mean) Pareto random variables. With the notion of majorization order, we show that a more diversified…
We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…
Among bivariate tail dependence measures, the tail dependence coefficient has emerged as the popular choice. Akin to the correlation matrix, a multivariate dependence measure is constructed using these bivariate measures, and this is…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…