Lígia Henriques-Rodrigues

arXiv2026

Long-Term Tail Modeling in Survival Analysis via Extended Generalized Pareto Distributions

We propose a class of extended generalized Pareto models for right-censored survival data, with particular emphasis on tail inference and long-term extrapolation. Our framework integrates extreme value theory and survival analysis, combining a generalized Pareto distribution with a flexible perturbation distribution on the unit interval. We consider three perturbation specifications: a parametric Beta model, a Bernstein polynomial estimator, and a histogram-based estimator. To facilitate direct comparison, all three models are fitted using a unified iterative procedure adapted to right censoring through Kaplan-Meier-based pseudo-observations. A Monte Carlo study evaluates finite-sample performance across different tail indices, censoring levels, sample sizes, and model complexities. The results reveal a trade-off between flexibility and stability: the Beta specification generally performs best for tail-index estimation, whereas the histogram estimator performs particularly well for scale estimation under low censoring. The Bernstein estimator shows intermediate performance and greater sensitivity to sample size and censoring. Applications to bladder cancer recurrence and heart-failure survival data show that models with very similar in-sample fits can nevertheless produce markedly different tail-index estimates and long-term extrapolations. These findings emphasize the importance of perturbation specification when extended generalized Pareto models are used for survival extrapolation under censoring.

stat.ME↗

arXiv2024

Improvements in the estimation of the Weibull tail coefficient -- a comparative study

The Weibull tail-coefficient (WTC) plays a crucial role in extreme value statistics when dealing with Weibull-type tails. Several distributions, such as normal, Gamma, Weibull, and Logistic distributions, exhibit this type of tail behaviour. The WTC, denoted by $θ$, is a parameter in a right-tail function of the form $ \bar F(x) :=1-F(x) =: {\rm e}^{-H(x)}$, where $H(x)=-\ln(1-F(x))$ represents a regularly varying cumulative hazard function with an index of regular variation equal to 1/$θ$, $θ\in\mathbb{R}^{+}$. The commonly used WTC-estimators in literature are often defined as functions of the log-excesses, making them closely related to estimators of the extreme value index (EVI) for Pareto-type tails. For a positive EVI, the classical estimator is the Hill estimator. Generalized means have been successfully employed in estimating the EVI, leading to reduction of bias and of root mean square error for appropriate threshold values. In this study, we propose and investigate new classes of WTC-estimators based on power $p$ of the log-excesses within a second-order framework. The performance of these new estimators is evaluated through a large-scale Monte-Carlo simulation study, comparing them with existing WTC-estimators available in the literature.

math.ST↗