Estimation of kernel density function using Kapur entropy

Abstract

Information-theoretic measures play a vital role in training learning systems. Many researchers proposed non-parametric entropy estimators that have applications in adaptive systems. In this work, a kernel density estimator using Kapur entropy of order α and type β has been proposed and discussed with the help of theorems and properties. From the results, it has been observed that the proposed density measure is consistent, minimum, and smooth for the probability density function (PDF) underlying given conditions and validated with the help of theorems and properties. The objective of the paper is to understand the theoretical viewpoint behind the underlying concept.