Improved lower bounds on the total variation distance for the Poisson approximation

Igal Sason

doi:10.1016/j.spl.2013.07.002

Improved lower bounds on the total variation distance for the Poisson approximation

Igal Sason

Electrical and Computer Engineering

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › 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. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.

Original language	English
Pages (from-to)	2422-2431
Number of pages	10
Journal	Statistics and Probability Letters
Volume	83
Issue number	10
DOIs	https://doi.org/10.1016/j.spl.2013.07.002
State	Published - Oct 2013

Keywords

Chen-Stein method
Poisson approximation
Total variation distance

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2013.07.002

Cite this

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title = "Improved lower bounds on the total variation distance for the Poisson approximation",

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. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.",

keywords = "Chen-Stein method, Poisson approximation, Total variation distance",

author = "Igal Sason",

note = "Funding Information: The anonymous reviewer is acknowledged for suggestions that led to improvement of the presentation of this paper. This research work was supported by the Israeli Science Foundation (ISF) , grant number 12/12 .",

year = "2013",

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doi = "10.1016/j.spl.2013.07.002",

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N1 - Funding Information: The anonymous reviewer is acknowledged for suggestions that led to improvement of the presentation of this paper. This research work was supported by the Israeli Science Foundation (ISF) , grant number 12/12 .

PY - 2013/10

Y1 - 2013/10

N2 - 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. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.

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. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.

KW - Chen-Stein method

KW - Poisson approximation

KW - Total variation distance

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U2 - 10.1016/j.spl.2013.07.002

DO - 10.1016/j.spl.2013.07.002

M3 - مقالة

SN - 0167-7152

VL - 83

SP - 2422

EP - 2431

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 10

ER -

Improved lower bounds on the total variation distance for the Poisson approximation

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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