An Analog-Digital Hardware for Parzen-Based Nonparametric Probability Density Estimation

Abstract

Probability estimation measures the likelihood of different outcomes in a statistical context. It commonly involves estimating either the parameters or the entire distribution of a random variable. Parametric approaches, where a specific functional form is assumed for data distribution, have been used in various fields, particularly in computational statistics for modeling and simulating physical phenomena. However, non-parametric methods have gained prominence, especially in machine learning and signal processing. These methods are focused on estimating or modeling probability density functions without relying on predefined parametric forms. It becomes crucial when faced with unknown or complex distributions, especially if parametric assumptions do not hold. This paper deals with the non-parametric method based on the Parzen window for probability density function estimation, a versatile approach applicable to univariate and multivariate data. Having a sufficient amount of data, this method provides reliable estimates, while at the same time, it is quite suitable for implementation. Considering the advantages of hardware implementations compared to software solutions, this paper introduces analog-digital hardware for the Parzen approach. The proposed solution avoids the need for sorting operations, which are typically challenging to implement in hardware. The simulation is performed using PSpice software (OrCad version 22.1) showing that the required processing time is under 420 ns.

Keywords

• Analog hardware
• non-parametric approach
• Parzen window
• probability density estimation