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

Omid Kharazmi; Narayanaswamy Balakrishnan

doi:10.3390/e23030363

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

Entropy (Basel). 2021 Mar 18;23(3):363. doi: 10.3390/e23030363.

Authors

Omid Kharazmi¹, Narayanaswamy Balakrishnan²

Affiliations

¹ Department of Statistics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, P.O. Box 518, Rafsanjan, Iran.
² Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada.

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: Bayes–Fisher information; Fisher information; Jensen–Shannon entropy; Kullback–Leibler divergence; chi-square divergence.