In this work, we further study the moving grating technique applied to halide perovskite thin-film materials. First, we show some problems that emerge when analyzing the experimental data with the classical formulation, which does not distinguish between free and trapped carriers and hence only gives average quantities for the transport parameters. We show that using a more general framework, taking into account the multiple trapping of carriers within a density of localized states, allows for an accurate description. Since it includes the density of states (DOS) of the material, it enables the possibility to test different DOS models proposed in the past for halide perovskite thin films. We check whether these models give rise to the type of curves we have measured under different experimental conditions. Finally, we propose a new model for the DOS in the forbidden gap, which results in the best fit found for the measurements performed. This allows us to give ranges of values for the parameters that define the DOS, which, as far as we know, are given for the first time.