This work provides physical insight into common statistical models for DC dielectric breakdown field strengths. Voltage step-up tests were performed on low density polyethylene films. The merits of generalizations to widely-used empirical Weibull models are discussed. The cumulative probability distributions of the breakdown fields were fit to standard two- and three-parameter Weibull distributions. Mixed two-parameter Weibull distributions, sometimes used in the literature to model multiple breakdown modes, were found to yield the best fits to the data. In addition, the same data were fit to a physically-motivated dual-defect mean field model incorporating both low- and high-energy defect modes with different defect densities; this produced a much better fit than single-defect mean field models. Values obtained for the mean defect energies and densities were within the ranges expected from independent determinations of these intrinsic materials properties. By incorporating these physics-based concepts into traditionally empirical models, their accuracy and utility can be extended. The mixed Weibull distribution and the dual-defect model predicted very similar cumulative distributions of LDPE breakdown data, suggesting that mixed Weibull distributions may reflect similar multiple defect modes used in dual-defect models. Theories of DC breakdown, based on distributions of microscopic defects in disordered insulating materials may provide improved guidance in understanding the physical origins of empirical parameters used in statistical methods to characterize breakdown properties.