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.