A Vector Generalized Linear Model for Trivariate Stochastic Episodes with Pareto and Geometric Marginals
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Authors
Luerken, Erick Lothar
Issue Date
2025
Type
Dissertation
Language
en_US
Keywords
Extreme Value Theory , Multivariate Models , Stochastic Processes , Vector GLM
Alternative Title
Abstract
Extreme weather, climate, and financial events are frequently featured in the news due to their significant impact on both human life and the environment. This work presents statistical modeling tools for analyzing such extreme events. We propose a multivariate model to describe events like storms, floods, heatwaves, and financial market crashes. The model incorporates covariates that influence the size or probability of these extreme events. Specifically, we implement a vector generalized linear model (VGLM), an extension of standard regression methods. We also develop parameter estimators, including theorems on their existence and uniqueness. To facilitate practical use, we have created a freely available computational package. In addition, we offer recommendations on best practices for handling common computational challenges in applying the model to real-world data. We demonstrate the effectiveness of our model by applying it to precipitation data in California and Nevada, achieving strong results.