Related papers: Sub-Weibull distributions: generalizing sub-Gaussi…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
Fertility plans, measured by the number of planned children, have been found to be affected by education and family background via complex tail dependencies. This challenge was previously met with the use of non-parametric jittering…
Nowadays in density estimation, posterior rates of convergence for location and location-scale mixtures of Gaussians are only known under light-tail assumptions; with better rates achieved by location mixtures. It is conjectured, but not…
In recent years, various notions of capacity and complexity have been proposed for characterizing the generalization properties of stochastic gradient descent (SGD) in deep learning. Some of the popular notions that correlate well with the…
In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance…
Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and…
The realized GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized…
The approach used by Kalashnikov and Tsitsiashvili for constructing upper bounds for the tail distribution of a geometric sum with subexponential summands is reconsidered. By expressing the problem in a more probabilistic light, several…
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,…
As well known, for a supercritical Galton-Watson process $Z_n$ whose offspring distribution has mean $m>1$, the ratio $W_n:=Z_n/m^n$ has a.s. limit, say $W$. We study tail behaviour of the distributions of $W_n$ and $W$ in the case where…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
We extend the class of tempered stable distributions first introduced in Rosinski 2007. Our new class allows for more structure and more variety of tail behaviors. We discuss various subclasses and the relation between them. To characterize…
Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…
In previous work Majda and McLaughlin computed explicit expressions for the $2N$th moments of a passive scalar advected by a linear shear flow in the form of an integral over ${\bf R}^N$. In this paper we first compute the asymptotics of…
Let $X$ be an $n\times n$ symmetric random matrix with independent but non-identically distributed entries. The deviation inequalities of the spectral norm of $X$ with Gaussian entries have been obtained by using the standard concentration…
A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…
In this paper we propose a new four-parameters distribution with increasing, decreasing, bathtub-shaped and unimodal failure rate, called as the exponentiated Weibull-Poisson (EWP) distribution. The new distribution arises on a latent…
In this paper we study a broad class of distribution functions which is defined by means of reflected generalized beta distribution. This class includes that of Beta-generated distribution as a special case. In particular, we use this class…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
In this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer…