Related papers: A New Distribution-Random Limit Normal Distributio…
We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply…
We develop two novel approaches for constructing skewed and bimodal flexible distributions that can effectively generalize classical symmetric distributions. We illustrate the application of introduced techniques by extending normal,…
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…
The tail index, indicating the degree of fatness of the tail distribution, is an important component of extreme value theory since it dominates the asymptotic distribution of extreme values such as the sample maximum. In this paper, we…
Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…
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…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
We introduce a novel family of projected distributions on the circle and the sphere, namely the circular and spherical projected Cauchy distributions, as promising alternatives for modelling circular and spherical data. The circular…
This paper introduces the multivariate tail-inflated normal (MTIN) distribution, an elliptical heavy-tails generalization of the multivariate normal (MN). The MTIN belongs to the family of MN scale mixtures by choosing a convenient…
Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the…
We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…
A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal,…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…
In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…
Discrete normal distributions are defined as the distributions with prescribed means and covariance matrices which maximize entropy on the integer lattice support. The set of discrete normal distributions form an exponential family with…
It was observed that the number of cases and deaths for infectious diseases were associated with heavy-tailed power law distributions such as the Pareto distribution. While Pareto distribution was widely used to model the cases and deaths…
For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…
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.…
In this paper, we proposed a new lifetime distribution namely generalized weighted Lindley (GLW) distribution. The GLW distribution is a useful generalization of the weighted Lindley distribution, which accommodates increasing, decreasing,…