Properties of discrete Fisher information: Cramer-Rao-type and log-Sobolev-type inequalities
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The Fisher information have connections with the standard deviation and the Shannon differential entropy through the Cramer-Rao bound and the log-Sobolev inequality. These inequalities hold for continuous distributions. In this paper, we introduce the Fisher information for discrete distributions (DFI) and show that the DFI satisfies the Cramer-Rao-type bound and the log-Sobolev-type inequality.
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