Improved lower bounds on the total variation distance for the Poisson approximation |
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Authors: | Igal Sason |
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Institution: | Department of Electrical Engineering, Technion, Haifa 32000, Israel |
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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. 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. |
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Keywords: | Chen–Stein method Poisson approximation Total variation distance |
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