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Improved estimation of discrete probability density functions using multirate models

For many decades, the problem of estimating a pdf based on measurements has been of interest to many researchers. Even though much work has been done in the area of pdf estimation, most of it was focused on the continuous case. In this paper, we propose a new model based approach for estimating a discrete probability density function. This approach is based on multirate dsp theory, and it has several advantages over the traditional histogram method. It is shown that this method yields an unbiased pdf estimate with small variance, which is guaranteed to have a smaller estimation error than the histogram. Simulation results are given, which show the merit of the proposed method.