Related papers: A simple alternative to the Crystal Ball function
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We…
We introduce a scalar-less anomaly free chiral gauge theory that serves as natural ultraviolet completion of models of fundamental composite (Goldstone) Higgs dynamics. The new theory is able to generate the top mass and furthermore…
In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…
Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
For the problem of estimating lower tail and upper tail copulas, we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method uses a multiplier bootstrap of the…
It was recently discovered that waves scattering off a $Q$-ball can extract energy from it. We present an analytical treatment of this process by adopting a multi-step function approximation for the background field, which yields…
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…
Steady-state pair correlations between inelastic granular beads in a vertically shaken, quasi two-dimensional cell can be mapped onto the particle correlations in a truly two-dimensional reference fluid in thermodynamic equilibrium. Using…
Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…
In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten [12] and Goldie [8] all discount factors in the model are mutually independent. We prove that the tails of the…
This is an epistemological approach to errors in both inference and risk management, leading to necessary structural properties for the probability distribution. Many mechanisms have been used to show the emergence of fat tails. Here we…
In this short note, we derive a precise tail expansion for Gaussian multiplicative chaos (GMC) associated to the 2d GFF on the unit disk with zero average on the unit circle (and variants). More specifically, we show that to first order the…
Scalar-tensor theories are the best motivated alternatives to general relativity and provide a mathematically consistent framework to test the various observable predictions. They can involve three functions of the scalar field: (i) a…
We call two copulas tail equivalent if their first-order approximations in the tail coincide. As a special case, a copula is called tail symmetric if it is tail equivalent to the associated survival copula. We propose a novel measure and…
There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.
This study explores the application of a two-level algorithm to enhance the signal-to-noise ratio of glueball calculations in four-dimensional $\mathrm{SU(3)}$ pure gauge theory. Our findings demonstrate that the statistical errors exhibit…
We give an alternative computation of the twisted second moment of critival values of class group $L$-functions attached to an imaginary quadratic field. The method avoids long calculations and yields the expected polynomial growth in the…
Edgeworth expansion provides higher-order corrections to the normal approximation for a probability distribution. The classical proof of Edgeworth expansion is via characteristic functions. As a powerful method for distributional…