Estimating catastrophic quantile levels for heavy-tailed distributions

DOI10.1016/j.insmatheco.2004.03.004zbMath1188.91237OpenAlexW2078221804MaRDI QIDQ977160

Jan Beirlant, Gunther Matthys, Emmanuel Delafosse, Armelle Guillou

Publication date: 20 June 2010

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.insmatheco.2004.03.004

zbMATH Keywords

Bias reductionCensoringExtreme quantilesPareto index

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Applications of statistics to actuarial sciences and financial mathematics (62P05) Statistical methods; risk measures (91G70) Probability distributions: general theory (60E05) Characterization and structure theory of statistical distributions (62E10)

Related Items (25)

Reduced-bias and partially reduced-bias mean-of-order-p value-at-risk estimation: a Monte-Carlo comparison and an application ⋮ Extreme quantile estimation for \(\beta\)-mixing time series and applications ⋮ Nonparametric estimation of the conditional tail index and extreme quantiles under random censoring ⋮ Bias correction in extreme value statistics with index around zero ⋮ Inference for intermediate Haezendonck-Goovaerts risk measure ⋮ A Mean-of-Order-$$p$$ Class of Value-at-Risk Estimators ⋮ ESTIMATION OF RISK MEASURES FROM HEAVY TAILED DISTRIBUTIONS ⋮ Semi-parametric estimation of the quintile share ratio index of inequality measure for heavy-tailed income distributions with index in the upper half of the unit interval ⋮ Earthquake parametric insurance with Bayesian spatial quantile regression ⋮ Semi-parametric second-order reduced-bias high quantile estimation ⋮ Extreme Value Theory and Statistics of Univariate Extremes: A Review ⋮ Nonparametric estimation of the conditional extreme-value index with random covariates and censoring ⋮ Improved estimators of tail index and extreme quantiles under dependence serials ⋮ Estimation of extreme values by the average conditional exceedance rate method ⋮ Bias-reduced extreme quantile estimators of Weibull tail-distributions ⋮ Improved reduced-bias tail index and quantile estimators ⋮ Pitfalls in using Weibull tailed distributions ⋮ Bias reduction for high quantiles ⋮ Extreme dependence of multivariate catastrophic losses ⋮ On univariate extreme value statistics and the estimation of reinsurance premiums ⋮ Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions ⋮ Goodness-of-fit test for tail copulas modeled by elliptical copulas ⋮ Bias-reduced estimators of the Weibull tail-coefficient ⋮ Adaptive Reduced-Bias Tail Index and VaR Estimation via the Bootstrap Methodology ⋮ Estimating the Probability of a Rare Event via Elliptical Copulas

Cites Work

• Unnamed Item
• Unnamed Item
• Extreme quantile estimation for dependent data, with applications to finance
• Almost sure convergence of a tail index estimator in the presence of censoring.
• On asymptotic normality of Hill's estimator for the exponent of regular variation
• Estimating tails of probability distributions
• A simple general approach to inference about the tail of a distribution
• On exponential representations of log-spacings of extreme order statistics
• Tail index estimation and an exponential regression model
• Selecting the optimal sample fraction in univariate extreme value estimation
• Estimating a tail exponent by modelling departure from a Pareto distribution
• On the estimation of high quantiles
• Pareto Index Estimation Under Moderate Right Censoring
• Almost sure convergence of the Hill estimator
• On Smooth Statistical Tail Functionals
• Estimation of Parameters and Larger Quantiles Based on the k Largest Observations

This page was built for publication: Estimating catastrophic quantile levels for heavy-tailed distributions