A new method to calculate and analyze coercivity distributions of measured acquisition/demagnetization curves of remanent magnetization is presented. The acquisition/demagnetization curves are linearized by rescaling both the field and the magnetization axes. An appropriate filtering of the linearized curves efficiently removes measurement errors prior to evaluating the coercivity distributions. The filtered coercivity distributions are modeled using a set of generalized probability density functions in order to estimate the contributions of different magnetic components. An error estimation is calculated for these functions with analytical and numerical methods in order to evaluate whether the model is significantly different from the measured data. Three sediment samples from Baldeggersee (Switzerland) and three samples of urban atmospheric particulate matter (PM) have been analyzed using this method. It is found that the coercivity distributions of some of the magnetic components show significant and consistent deviations from a logarithmic Gaussian function. Large deviations are found also in the coercivity distributions of theoretical AF demagnetization curves of single-domain and multidomain particles. Constraints in the shape of model functions affect the identification and quantification of magnetic components from remanent magnetization curves and should be avoided as far as possible. The generalized probability density function presented in this paper is suitable for appropriate modeling of Gaussian and a large number of non-Gaussian coercivity distributions.