Generalized piecewise non-linear bounded model for variables on [0, 1]

We propose a general class of models for analyzing continuous bounded data, based on a segmented decomposition of the support by partitioning the interval into an arbitrary number of non-linear segments, each associated with a distinct probability density function with bounded support [0,1]. The flexibility of the proposed model makes it a useful tool for various modelling purposes. The proposed density function can be expressed as a mixture of density functions. A special model (when each baseline density is symmetric quadratic) is investigated in detail. The properties of the model are investigated, and the parameter estimation procedure for its parameters is derived using a hybrid approach, and its good performance has been evaluated by means of Monte Carlo simulations. We provide an application to show the modelling competence of the proposed distribution when the dataset shows multimodality, and we compare it with mixtures of Beta distributions, with our proposed model presenting better results.