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Joint modeling of low and high extremes using a multivariate extended generalized Pareto distribution

N Alotaibi, M Sainsbury-Dale, P Naveau… - arXiv preprint arXiv …, 2025 - arxiv.org
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… , with key parameters separately controlling dependence in each joint tail; and (3) the model allows for fast simulation and is thus amenable to simulation-based inference. …

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@article{2509.05982v1,
Author        = {Noura Alotaibi and Matthew Sainsbury-Dale and Philippe Naveau and Carlo Gaetan and Raphaël Huser},
Title         = {Joint modeling of low and high extremes using a multivariate extended
  generalized Pareto distribution},
Eprint        = {2509.05982v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.ME},
Abstract      = {In most risk assessment studies, it is important to accurately capture the
entire distribution of the multivariate random vector of interest from low to
high values. For example, in climate sciences, low precipitation events may
lead to droughts, while heavy rainfall may generate large floods, and both of
these extreme scenarios can have major impacts on the safety of people and
infrastructure, as well as agricultural or other economic sectors. In the
univariate case, the extended generalized Pareto distribution (eGPD) was
specifically developed to accurately model low, moderate, and high
precipitation intensities, while bypassing the threshold selection procedure
usually conducted in extreme-value analyses. In this work, we extend this
approach to the multivariate case. The proposed multivariate eGPD has the
following appealing properties: (1) its marginal distributions behave like
univariate eGPDs; (2) its lower and upper joint tails comply with multivariate
extreme-value theory, with key parameters separately controlling dependence in
each joint tail; and (3) the model allows for fast simulation and is thus
amenable to simulation-based inference. We propose estimating model parameters
by leveraging modern neural approaches, where a neural network, once trained,
can provide point estimates, credible intervals, or full posterior
approximations in a fraction of a second. Our new methodology is illustrated by
application to daily rainfall times series data from the Netherlands. The
proposed model is shown to provide satisfactory marginal and dependence fits
from low to high quantiles.},
Year          = {2025},
Month         = {Sep},
Url           = {http://arxiv.org/abs/2509.05982v1},
File          = {2509.05982v1.pdf}
}

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