Extended generalised Pareto models for tail estimation

By Ioannis Papastathopoulos, Jonathan A. Tawn. 2011

116 citations recorded by the source corpus.

The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the model fits the data well. Sometimes, few observations of a measurement process might be recorded in applications and so selecting a high quantile of the sample as the threshold leads to almost no exceedances. In this paper we propose extensions of the generalised Pareto distribution that incorporate an additional shape parameter while keeping the tail behaviour unaffected. The inclusion of this parameter offers additional structure for the main body of the distribution, improves the stability of the modified scale, tail index and return level estimates to threshold choice and allows a lower threshold to be selected. We illustrate the benefits of the proposed models with a simulation study and two case studies.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5129256ddef422332ec16a6dd67feeaefe80e8aa

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Citations in the corpus

Stochastic generation of multi-site daily precipitation focusing on extreme events (2018, background): “This distribution was first proposed by Papastathopoulos and Tawn (2013), who referred to it as an extended GP-Type III distribution, and it has since been shown to adequately model the whole range of precipitation intensities (Naveau et al., 2016).”
INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018, background): “In future work, it would be interesting to replace the generalized Pareto distribution by more ﬂexible sub-asymptotic tail models (see, e.g., Papastathopoulos and Tawn, 2013; Naveau et al. , 2016), which could potentially be applied at much lower thresholds.”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, background): “0 as #0 and = 0 xed, leading to a Gaussian limit in analogy to the Student model. Model 2 has similarities with univariate tail models such as the extended generalized Pareto distributions proposed byPapastathopoulos and Tawn (2013) andNaveau et al.(2016), which improve exibility over the classical ”
Automated threshold selection for extreme value analysis via ordered goodness-of-fit tests with adjustment for false discovery rate (2018, background): “If an indirect solution is desired, one may relax the distributional assumptions [e.g., Papastathopoulos and Tawn (2013), Nadarajah and Eljabri (2013)] and follow the same procedure.”