Non-parametric estimation of probability density functions via a simple interpolation filter

In this paper we discuss non-parametric estimation of the probability density function (PDF) of a univariate random variable. This problem has been the subject of a vast amount of scientific literature in many domains: while statisticians are mainly interested in the analysis of the properties of proposed estimators, engineers treat the histogram as a ready-to-use tool for dataset analysis. By considering histogram data as a numerical sequence, a simple PDF estimator is presented in this paper. It is based on basic notions related to the reconstruction of a continuous-time signal from a sequence of samples and it is as accurate as kernel-based estimators, widely adopted in the statistical literature. The major properties of the proposed PDF estimator are discussed and then verified by simulations related to the common case of a normal density function.