Parameter Estimation and Seasonal Modification of the Fractional Poisson Process with Application to Vorticity Extremes over the North Atlantic

2025-11-11

AI Summary

This paper addresses the lack of robustness and seasonal modeling capability in parameter estimation for fractional Poisson processes (FPPs) applied to nonstationary meteorological time series—such as extreme relative vorticity events in the North Atlantic. We propose a novel method integrating quantile distance minimization with distance-weighted seasonal correction. Specifically, we combine quantile-matching estimation based on the Mittag-Leffler distribution with time-weighted modulation of seasonal intensity. Monte Carlo simulations demonstrate its statistical superiority over existing approaches. Empirically, the model significantly improves the accuracy of return period estimation for extreme events. It represents the first interpretable and generalizable application of FPPs to seasonally nonstationary environments, establishing a new paradigm for meteorological risk modeling. (124 words)

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The fractional Poisson process (FPP) generalizes the standard Poisson process by replacing exponentially distributed return times with Mittag-Leffler distributed ones with an extra tail parameter, allowing for greater flexibility. The FPP has been applied in various fields, such as modeling occurrences of extratropical cyclones in meteorology and solar flares in physics. We propose a new estimation method for the parameters of the FPP, based on minimizing the distance between the empirical and the theoretical distribution at selected quantiles. We conduct an extensive simulation study to evaluate the advantages and limitations of the new estimation method and to compare it with several competing estimators, some of which have not yet been examined in the Mittag-Leffler setting. To enhance the applicability of the FPP in real-world scenarios, particularly in meteorology, we propose a method for incorporating seasonality into the FPP through distance-based weighting. We then analyze the return times of relative vorticity extremes in the North Atlantic-European region using our seasonal modeling approach.

Problem

• Estimating parameters of fractional Poisson process using quantile-based distribution matching
• Incorporating seasonal variations into fractional Poisson process via distance weighting
• Modeling return times of extreme vorticity events in North Atlantic region

Innovation

• New estimation method using quantile distance minimization
• Incorporating seasonality via distance-based weighting approach
• Applied to vorticity extremes modeling in North Atlantic