Abstract A novel model is presented that incorporates the Arrhenius integral into one of the generalized extreme value (GEV) distributions to describe the pyrolysis of complex feedstocks. The model differs in structure from distributed activation energy models (DAEM), and its self-variable differs from Weibull mixture models. It is found that all first order reactions, regardless of their activation energies and pre-exponential factors, can be best modeled by a unified Frechet (inverse Weibull) minima distribution versus a reaction progress factor, followed by the Gumbel maxima and classical Weibull minima distributions. When applied to thermogravimetric analysis (TGA), the peak temperature is linked to a characteristic reaction progress factor, which largely accounts for the increase of peak temperatures with increasing heating rate. The model is able to deconvolute the contributions of multiple components in the sample and to estimate kinetic parameters for individual components by least squares regression. A correlation derived from the model can be used to evaluate apparent activation energy based on the shift in peak temperature as the heating rate varies, similar to the Kissinger method and its variants. The present work provides not only a different model framework, but also new perspective on the interactions between the statistical distribution of material properties and reactivity.