Time interval of slow polarization reversal in ferroelectric thin films is broadened over more than two decades to disobey the classical Kolmogorov-A vrami-Ishibashi (KAI) equation as the applied field approaches the coercive field of domain switching. The assumption of a Lorentzian distribution of logarithmic waiting times of reversed domain nucleation in this equation can resolve this dilemma. In our work, we explain this equation from the coercive-voltage distribution in thin films, and derive a similar function to describe slow polarization reversal from the consideration of a long-time imprint effect rather than the KAI model.