We investigated the time-dependent polarization switching behaviors of (111)-preferred polycrystalline Pb(ZrxTi1-x)O3 thin films with various Zr concentrations. We could explain all the polarization switching behaviors well by assuming Lorentzian distributions in the logarithmic polarization switching time [refer to J. Y. Jo etal, Phys. Rev. Lett. 99, 267602 (2007)]. Based on this analysis, we found that the Zr ion substitution for Ti ions would induce broad distributions in the local field due to defect dipoles, which makes the ferroelectric domain switching occur more easily.