Related papers: A Note on Computing Extreme Tail Probabilities of …
An efficient adaptive direct numerical integration (DNI) algorithm is developed for computing high quantiles and conditional Value at Risk (CVaR) of compound distributions using characteristic functions. A key innovation of the numerical…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
In 2017-2020 Jordanova and co-authors investigate probabilities for p-outside values and determine them in many particular cases. They show that these probabilities are closely related to the concept for heavy tails. Tukey's boxplots are…
How to estimate the uncertainty of a given model is a crucial problem. Current calibration techniques treat different classes equally and thus implicitly assume that the distribution of training data is balanced, but ignore the fact that…
Electrical grid congestion is a growing challenge in Europe, driving the need for accurate prediction of load, particularly of peak load. Non-time-resolved models of peak load offer the advantages of simplicity and compactness, and among…
The use of summary statistics beyond the two-point correlation function to analyze the non-Gaussian clustering on small scales is an active field of research in cosmology. In this paper, we explore a set of new summary statistics -- the…
Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms,…
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. This result…
We introduce a method for the estimation of uncertainties in density-functional-theory (DFT) calculations for atomistic systems. The method is based on the construction of an uncertainty-aware functional distribution (UAFD) in a space…
Causality is widely used in fairness analysis to prevent discrimination on sensitive attributes, such as genders in career recruitment and races in crime prediction. However, the current data-based Potential Outcomes Framework (POF) often…
In this paper, we obtain various series and asymptotic expansions involving the modified Bessel function of the second kind for the normal inverse Gaussian cumulative distribution function. The new expansions accelerate computations,…
Uncertainty estimation is critical for cost-sensitive deep-learning applications (i.e. disease diagnosis). It is very challenging partly due to the inaccessibility of uncertainty groundtruth in most datasets. Previous works proposed to…
In this paper, the multivariate tail covariance (MTCov) for generalized skew-elliptical distributions is considered. Some special cases for this distribution, such as generalized skew-normal, generalized skew student-t, generalized…
Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…
We introduce a new type of graphical model called a "cumulative distribution network" (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about…
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…
This paper proposes a nonparametric multivariate density forecast model based on deep learning. It not only offers the whole marginal distribution of each random variable in forecasting targets, but also reveals the future correlation…
In this correspondence, we point out two typographical errors in Chai and Tjhung's paper and we offer the correct formula of the unified Laguerre polynomial-series-based cumulative distribution function (cdf) for small-scale fading…
Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as…
We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…