Long-Term Tail Modeling in Survival Analysis via Extended Generalized Pareto Distributions
Abstract
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.
Related
- Pick-up sticks problems for exponential and Pareto distributions
- Skewness and Kurtosis for Heavy-Tailed Distributions: A Comparison of Mean Absolute Deviation and L-Moment Approaches for Pareto and Extreme-Value Families
- Tail expectile estimation in the semiparametric Generalized Pareto model
- Extended One-Liners for the Gamma, Poisson, and Binomial Distributions
- Generalized pseudo-product structures and finite type distributions via abnormal extremals
BibTeX
@misc{janotti2026longterm,
title = {{Long-Term Tail Modeling in Survival Analysis via Extended Generalized Pareto Distributions}},
author = {Eduardo Janotti and Lígia Henriques-Rodrigues and Antonio Carlos Pedroso de Lima},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28321},
eprint = {2609.28321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28321},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Long-Term Tail Modeling in Survival Analysis via Extended Generalized Pareto Distributions
AU - Eduardo Janotti
AU - Lígia Henriques-Rodrigues
AU - Antonio Carlos Pedroso de Lima
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28321
UR - https://arxiv.org/abs/2609.28321
AB - 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.
ER -