IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation
نویسنده
چکیده
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.
منابع مشابه
IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES An Information-Theoretic Perspective of the Poisson Approximation via the Chen- Stein Method
The first part of this work considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random variable with the same mean are derived via the Chen-Stein method. The second part of this work derives new lower bounds on the total variat...
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