Cramér-Rao-type Bound and Stam's Inequality for Discrete Random Variables

04/29/2019

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by   Tomohiro Nishiyama, et al.

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The variance and the entropy power of a continuous random variable are bounded from below by the reciprocal of its Fisher information through the Cramér-Rao bound and the Stam's inequality respectively. In this note, we introduce the Fisher information for discrete random variables and derive the discrete Cramér-Rao-type bound and the discrete Stam's inequality.