Discrete Versions of Jensen–Fisher, Fisher and Bayes–Fisher Information Measures of Finite Mixture Distributions

Abstract

In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback–Leibler, Jeffreys and Jensen–Shannon divergences.

Keywords

• Fisher information
• Bayes–Fisher information
• chi-square divergence
• Kullback–Leibler divergence
• Jensen–Shannon entropy