The potential applications of dispersive kinetic models range from solid-state conversions to gas-phase chemical physics and to microbiology. Here, the derivation and application of two such models, for use in solid-state applications, is presented. The models are based on the concept of a Maxwell-Boltzmann distribution of activation energies. The ability of the models to fit/explain an assortment of asymmetric, sigmoidal conversion-versus-time transients presented in the recent literature, as well as to provide physicochemical interpretations of the kinetics via the two fit parameters, alpha and beta, makes them a powerful tool for understanding nucleation/denucleation rate-limited processes that are involved in many phase transformations, dissolutions and crystallizations.