相关论文: Taming the Long Tail of Deep Probabilistic Forecas…

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 consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…

This note presents an operational measure of fat-tailedness for univariate probability distributions, in $[0,1]$ where 0 is maximally thin-tailed (Gaussian) and 1 is maximally fat-tailed. Among others,1) it helps assess the sample size…

Conformal prediction has emerged as a rigorous means of providing deep learning models with reliable uncertainty estimates and safety guarantees. Yet, its performance is known to degrade under distribution shift and long-tailed class…

Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…

The imbalance (or long-tail) is the nature of many real-world data distributions, which often induces the undesirable bias of deep classification models toward frequent classes, resulting in poor performance for tail classes. In this paper,…

Modeling and predicting extreme movements in GDP is notoriously difficult and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large…

While the estimation of risk is an important question in the daily business of banking and insurance, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and…

Climate extremes such as floods, storms, and heatwaves have caused severe economic and human losses across Europe in recent decades. To support the European Union's climate resilience efforts, we propose a statistical framework for…

We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace…

I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward,…

We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…

Accurate modeling is essential in integer-valued real phenomena, including the distribution of entire data, zero-inflated (ZI) data, and discrete exceedances. The Poisson and Negative Binomial distributions, along with their ZI variants,…

A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the…

In recent years several attempts have been made to extend tail modelling towards the modal part of the data. Frigessi et al. (2002) introduced dynamic mixtures of two components with a weight function {\pi} = {\pi}(x) smoothly connecting…

We investigate the relation between moments and tails of heavy-tailed (in particular, Pareto-type) distributions. We also discuss the sharpness of our results in a number of examples under certain regularity conditions like log-convexity.…

The double Pareto distribution is a heavy-tailed distribution with a power-law tail, that is generated via geometric Brownian motion with an exponentially distributed observation time. In this study, we examine a modified model wherein the…

While the {estimation} of risk is an important question in the daily business of banking and insurance, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and…

This paper presents a novel semiparametric method to study the effects of extreme events on binary outcomes and subsequently forecast future outcomes. Our approach, based on Bayes' theorem and regularly varying (RV) functions, facilitates a…

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…