Improved lower bounds on the total variation distance and relative entropy for the Poisson approximation

Igal Sason

doi:10.1109/ITA.2013.6502974

Improved lower bounds on the total variation distance and relative entropy for the Poisson approximation

Igal Sason

Electrical and Computer Engineering

Technion - Israel Institute of Technology

Research output: Contribution to conference › Paper › peer-review

Abstract

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. Corresponding lower bounds on the relative entropy are derived, based on the lower bounds on the total variation distance and an existing distribution-dependent refinement of Pinsker's inequality. Two uses of these bounds are finally outlined. The full version for this shortened paper is available at http://arxiv.org/abs/1206.6811.

Original language	English
Pages	360-363
Number of pages	4
DOIs	https://doi.org/10.1109/ITA.2013.6502974
State	Published - 2013
Event	2013 Information Theory and Applications Workshop, ITA 2013 - San Diego, CA, United States Duration: 10 Feb 2013 → 15 Feb 2013

Conference

Conference	2013 Information Theory and Applications Workshop, ITA 2013
Country/Territory	United States
City	San Diego, CA
Period	10/02/13 → 15/02/13

Keywords

Chen-Stein method
Poisson approximation
relative entropy
total variation distance

All Science Journal Classification (ASJC) codes

Computer Science Applications
Information Systems

Access to Document

10.1109/ITA.2013.6502974

Cite this

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abstract = "New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. Corresponding lower bounds on the relative entropy are derived, based on the lower bounds on the total variation distance and an existing distribution-dependent refinement of Pinsker's inequality. Two uses of these bounds are finally outlined. The full version for this shortened paper is available at http://arxiv.org/abs/1206.6811.",

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AB - New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. Corresponding lower bounds on the relative entropy are derived, based on the lower bounds on the total variation distance and an existing distribution-dependent refinement of Pinsker's inequality. Two uses of these bounds are finally outlined. The full version for this shortened paper is available at http://arxiv.org/abs/1206.6811.

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KW - relative entropy

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ER -

Improved lower bounds on the total variation distance and relative entropy for the Poisson approximation

Abstract

Conference

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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Cite this