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Abstract The growing frequency and size of wildfires across the US necessitates accurate quantitative assessment of evolving wildfire behavior to predict risk from future extreme wildfires. We build a joint model of wildfire counts and burned areas, regressing key model parameters on climate and demographic covariates. We use extended generalized Pareto distributions to model the full distribution of burned areas, capturing both moderate and extreme sizes, while leveraging extreme value theory to focus particularly on the right tail. We model wildfire counts with a zero‐inflated negative binomial model, and join the wildfire counts and burned areas sub‐models using a temporally‐varying shared random effect. Our model successfully captures the trends of wildfire counts and burned areas. By investigating the predictive power of different sets of covariates, we find that fire indices are better predictors of wildfire burned area behavior than individual climate covariates, whereas climate covariates are influential drivers of wildfire occurrence behavior. 

Summary The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighbourhood of the true shape parameter.