Related papers: Functional Peaks-over-threshold Analysis
We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…
This paper contributes to answering a question that is of crucial importance in risk management and extreme value theory: How to select the threshold above which one assumes that the tail of a distribution follows a generalized Pareto…
The multivariate generalized Pareto distribution (mGPD) is a common method for modeling extreme threshold exceedance probabilities in environmental and financial risk management. Despite its broad applicability, mGPD faces challenges due to…
Predicting the occurrence of tail events is of great importance in financial risk management. By employing the method of peak-over-threshold (POT) to identify the financial extremes, we perform a recurrence interval analysis (RIA) on these…
Modelling of precipitation, including extremes, is important for hydrological and agricultural applications. Traditionally, because of large sample properties for data over a large threshold value, generalised Pareto (GP) distributions are…
Power law distributions, in particular Pareto distributions, describe data across diverse areas of study. We have developed a package in R to estimate the tail index for such datasets focusing on speed (in particular with large datasets),…
For extreme value estimation we propose to use a model with a Dirichlet process mixture of gamma densities in the center and generalized Pareto densities for the tails. Due to the randomness in the center and a heavy tailed density in the…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
We present the winning strategy for the EVA2025 Data Challenge, which aimed to estimate the probability of extreme precipitation events. These events occurred at most once in the dataset making the challenge fundamentally one of…
Accurate modeling of daily rainfall, encompassing both dry and wet days as well as extreme precipitation events, is critical for robust hydrological and climatological analyses. This study proposes a zero-inflated extended generalized…
A widely used tool in the study of risk, insurance and extreme values is the mean excess plot. One use is for validating a generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects…
Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…
We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
Statistical modelling of spatial extreme events has gained increasing attention over the last few decades with max-stable processes, and more recently $r$-Pareto processes, becoming the reference tools for the statistical analysis of…
The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
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…
A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…