Related papers: Modelling extreme claims via composite models and …
In samples from a heavy-tailed distribution a second-order approximation is often use to approximate the tail function. Based on the parameters of the approximation, an optimal sample fraction can be estimated which is then used to estimate…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
Designs conditions for marine structures are typically informed by threshold-based extreme value analyses of oceanographic variables, in which excesses of a high threshold are modelled by a generalized Pareto (GP) distribution. Too low a…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
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…
The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the…
This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for…
The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses. However, when data…
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 notoriously difficult challenge in extreme value theory is the choice of the number $k\ll n$, where $n$ is the total sample size, of extreme data points to consider for inference of tail quantities. Existing theoretical guarantees for…
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…
Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…
Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton…
Conventional methods for extreme event estimation rely on well-chosen parametric models asymptotically justified from extreme value theory (EVT). These methods, while powerful and theoretically grounded, could however encounter a difficult…
The statistical modeling of discrete extremes has received less attention than their continuous counterparts in the Extreme Value Theory (EVT) literature. One approach to the transition from continuous to discrete extremes is the modeling…
In many applied fields it is desired to make predictions with the aim of assessing the plausibility of more severe events than those already recorded to safeguard against calamities that have not yet occurred. This problem can be analysed…
Insurance products frequently cover significant claims arising from a variety of sources. To model losses from these products accurately, actuarial models must account for high-severity claims. A widely used strategy is to apply a mixture…
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 we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF)…
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…