Orthogonal parametrisations of Extreme-Value distributions

2026-02-18

AI Summary

This study addresses the instability and poor interpretability of parameter estimates in extreme value distributions under small-sample settings, which undermine the reliability of risk assessments. For the first time, the authors systematically apply the orthogonal parametrization theory of Cox and Reid (1987) to the generalized extreme value, generalized Pareto, and Gumbel distributions, proposing an orthogonal reparameterization approach that aligns model parameters more closely with practical modeling objectives. Simulation experiments demonstrate that this method substantially enhances both the stability and interpretability of parameter estimates in small samples, thereby providing a more robust statistical foundation for extreme value modeling.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is particularly problematic given the fact that often times these distributions are fitted to small samples. Furthermore, the distribution's parameters are generally not directly interpretable and not the key aim of the estimation. We present several orthogonal reparametrisations of the main extreme-value distributions, key in the modelling of rare events. In particular, we apply the theory developed in Cox and Reid (1987) to the Generalised Extreme-Value, Generalised Pareto, and Gumbel distributions. We illustrate the principal advantage of these reparametrisations in a simulation study.

Problem

• Extreme-Value distributions
• parameter instability
• small samples
• parameter interpretability
• orthogonal parametrisation

Innovation

• orthogonal parametrisation
• extreme-value distributions
• Cox-Reid adjustment
• statistical inference
• reparameterisation