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.
Highlights
Over the last seven decades, several different criteria have been introduced in the literature for measuring uncertainty in a probabilistic model
We show that discrete Jensen–Fisher information (DJFI) measure can be represented based on the mixture of discrete Fisher information distance measures
We show that the discrete Jensen–Fisher information measure can be obtained based on mixtures of Fisher information distances
Summary
Over the last seven decades, several different criteria have been introduced in the literature for measuring uncertainty in a probabilistic model. With regard to informational properties of finite mixture models, one may refer to Contreras-Reyes and Cortés [12] and Abid et al [13] These authors have provided upper and lower bounds for Shannon and Rényi entropies of non-gaussian finite mixtures, skewnormal and skew-t distributions, respectively. For this purpose, we first define discrete version of Jensen–Fisher information for two PMFs P and Q, and provide some results concerning this new information measure. Pn. The second purpose of this work is to study Fisher and Bayes–Fisher information measures for the mixing parameter of a finite mixture probability mass function.
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