Publications (20)
Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case
Jan Beirlant, Andrzej Kijko, Tom Reynkens +1
The area-characteristic, maximum possible earthquake magnitude is required by the earthquake engineering community, disaster management agencies and the insurance industry. T…
Non-parametric cure models through extreme-value tail estimation
Jan Beirlant, Martin Bladt, Ingrid Van Keilegom
In survival analysis, the estimation of the proportion of subjects who will never experience the event of interest, termed the cure rate, has received considerable attention recent…
Fitting tails affected by truncation
Jan Beirlant, Isabel Fraga Alves, Tom Reynkens
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncati…
A new class of copula regression models for modelling multivariate heavy-tailed data
Zhengxiao Li, Jan Beirlant, Liang Yang
A new class of copulas, termed the MGL copula class, is introduced. The new copula originates from extracting the dependence function of the multivariate generalized log-Moyal-gamm…
Bias Reduced Peaks over Threshold Tail Estimation
Jan Beirlant, Gaonyalelwe Maribe, Philippe Naveau +1
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 wi…
Combined Tail Estimation Using Censored Data and Expert Information
Martin Bladt, Hansjoerg Albrecher, Jan Beirlant
We study tail estimation in Pareto-like settings for datasets with a high percentage of randomly right-censored data, and where some expert information on the tail index is availab…
Statistics of Extremes for the Insurance Industry
Hansjoerg Albrecher, Jan Beirlant
We provide a survey of how techniques developed for the modelling of extremes naturally matter in insurance, and how they need to and can be adapted for the insurance applications.…
Estimation of the extreme value index in a censorship framework: asymptotic and finite sample behaviour
Jan Beirlant, Julien Worms, Rym Worms
We revisit the estimation of the extreme value index for randomly censored data from a heavy tailed distribution. We introduce a new class of estimators which encompasses earlier p…
Modelling Censored Losses Using Splicing: a Global Fit Strategy With Mixed Erlang and Extreme Value Distributions
Tom Reynkens, Roel Verbelen, Jan Beirlant +1
In risk analysis, a global fit that appropriately captures the body and the tail of the distribution of losses is essential. Modelling the whole range of the losses using a standar…
Tempered Pareto-type modelling using Weibull distributions
Jose Carlos Araujo Acuna, Hansjoerg Albrecher, Jan Beirlant
In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are…
Threshold selection and trimming in extremes
Martin Bladt, Hansjoerg Albrecher, Jan Beirlant
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…
Second-order refined peaks-over-threshold modelling for heavy-tailed distributions
Jan Beirlant, Elisabeth Joossens, Johan Segers
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typicall…
Trimmed extreme value estimators for censored heavy-tailed data
Martin Bladt, Hansjoerg Albrecher, Jan Beirlant
We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance obser…
Generalizing the log-Moyal distribution and regression models for heavy tailed loss data
Zhengxiao Li, Jan Beirlant, Shengwang Meng
Catastrophic loss data are known to be heavy-tailed. Practitioners then need models that are able to capture both tail and modal parts of claim data. To this purpose, a new paramet…
Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications
Jan Beirlant, Gaonyalelwe Maribe, Andrehette Verster
The subject of tail estimation for randomly censored data from a heavy tailed distribution receives growing attention, motivated by applications for instance in actuarial statistic…
Reducing MSE in estimation of heavy tails: a Bayesian approach
Gaonyalelwe Maribe, Andréhette Verster, Jan Beirlant
Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE)…
Center-outward quantiles and the measurement of multivariate risk
Jan Beirlant, Sven Buitendag, Eustasio del Bario +1
All multivariate extensions of the univariate theory of risk measurement run into the same fundamental problem of the absence, in dimension d > 1, of a canonical ordering of Rd. Ba…
Tail fitting for truncated and non-truncated Pareto-type distributions
Jan Beirlant, Isabel Fraga Alves, Ivette Gomes
Recently some papers, such as Aban, Meerschaert and Panorska (2006), Nuyts (2010) and Clark (2013), have drawn attention to possible truncation in Pareto tail modelling. Sometimes…
Extreme value statistics for truncated Pareto-type distributions
Jan Beirlant, Isabel Fraga Alves, Ivette Gomes +1
Recently attention has been drawn to practical problems with the use of unbounded Pareto distributions, for instance when there are natural upper bounds that truncate the probabili…
Outlier detection and a tail-adjusted boxplot based on extreme value theory
Shrijita Bhattacharya, Jan Beirlant
Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven metho…