Related papers: Tail fitting for truncated and non-truncated Paret…

The paper suggests a simple method of deriving minimax lower bounds to the accuracy of statistical inference on heavy tails. A well-known result by Hall and Welsh (Ann. Statist. 12 (1984) 1079-1084) states that if $\hat{\alpha}_n$ is an…

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…

One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…

Accurately quantifying tail risks-rare but high-impact events such as financial crashes or extreme weather-is a central challenge in risk management, with serially dependent data. We develop a Bayesian framework based on the Generalized…

The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of…

We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account…

The central limit theorem introduced by Stute [The central limit theorem under random censorship. Ann. Statist. 1995; 23: 422-439] does not hold for some class of heavy-tailed distributions. In this paper, we make use of the extreme value…

We consider the problem of finding the optimal upper bound for the tail probability of a sum of $k$ nonnegative, independent and identically distributed random variables with given mean $x$. For $k=1$ the answer is given by Markov's…

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate…

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…

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method…

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,…

The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with…

We introduce a new actuarial tail-shape index, the $\theta$-index, based on a probability equal level relationship between Value at Risk and Expected Shortfall. The index is defined at each tail probability level as the parameter value for…

We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…

Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect…

We consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of…

In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale under norming sequence 1/n, as in the classical Law of Large Numbers (LLN), by means of martingale differences…