Cram\'{e}r-Rao-type Bound and Stam's Inequality for Discrete Random Variables

Tomohiro Nishiyama

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arXiv · 1904.12704

Cram\'{e}r-Rao-type Bound and Stam's Inequality for Discrete Random Variables

Tomohiro Nishiyama

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Abstract

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

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Tomohiro Nishiyama. 2019-04-29. Cram\'{e}r-Rao-type Bound and Stam's Inequality for Discrete Random Variables. https://arxiv.org/abs/1904.12704

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