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

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.