A multirate DSP model for estimation of discrete probability density functions

Abstract

The problem of estimating a probability density function (PDF) from measurements has been widely studied by many researchers. Even though much work has been done in the area of PDF estimation, most of it was focused on the continuous case. We propose a new model-based approach for modeling and estimating discrete probability density functions or probability mass functions. This approach is based on multirate signal processing theory, and it has several advantages over the conventional histogram method. We illustrate the PDF estimation procedure and analyze the statistical properties of the PDF estimates. Based on this model, a novel scheme is introduced that can be used for estimating the PDF in the presence of noise. Furthermore, the proposed ideas are extended to the more general case of estimating multivariate PDFs. Finally, we also consider practical issues such as optimizing the coefficients of a digital filter, which is an integral part of the model. This allows us to apply the proposed model to solve real-world problems. Simulation results are given where appropriate in order to demonstrate the ideas.