Artificial neural networks applied for estimating a probability density function

Abstract

The estimate of the probability density function or probability mass function of an unknown stochastic process is a very important preliminary step for any further elaboration. Most of the traditional approaches to this problem perform a preliminary choice of a parametric mathematical model of the function to estimate and a subsequent fitting on its parameters. To this aim some a-priori knowledge and/or assumptions on the phenomenon under consideration are needed. In this paper an alternative approach is proposed, which does not require any assumption on the available data, as it extracts the probability density function from the output of a neural network, that is trained with a suitable database including the original data and some ad hoc created data with known distribution. The results of the tests performed on synthetic and industrial databases are described and discussed in the paper.