Related papers: Estimating failure probabilities
From environmental sciences to finance, there is a growing demand for methods that can assess the risks of extreme events beyond those observed in available data. Extrapolating extreme events beyond the range of the data is not obvious.…
Extreme value analysis for time series is often based on the block maxima method, in particular for environmental applications. In the classical univariate case, the latter is based on fitting an extreme-value distribution to the sample of…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
In many application areas of extreme value theory, the variables of interest are not directly observable but instead contain errors. In this article, we quantify the effect of these errors in moment-based extreme value index estimation, and…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an…
In the multivariate setting, estimates of extremal risk measures are important in many contexts, such as environmental planning and structural engineering. In this paper, we propose new estimation methods for extremal bivariate return…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
Verifying probabilistic forecasts for extreme events is a highly active research area because popular media and public opinions are naturally focused on extreme events, and biased conclusions are readily made. In this context, classical…
Risk-sensitive reinforcement learning (RL) has garnered significant attention in recent years due to the growing interest in deploying RL agents in real-world scenarios. A critical aspect of risk awareness involves modeling highly rare risk…
The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of…
Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit-state function, which depends on the solution of a partial…
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…
We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk present in the components of a multivariate time series are often driven by the same underlying factors, such…