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Exact values and sharp estimates for the total variation distance between binomial and Poisson distributions
- Part of
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- Journal:
- Advances in Applied Probability / Volume 40 / Issue 4 / December 2008
- Published online by Cambridge University Press:
- 01 July 2016, pp. 1033-1047
- Print publication:
- December 2008
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- Article
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We present a method to obtain both exact values and sharp estimates for the total variation distance between binomial and Poisson distributions with the same mean λ. We give a simple efficient algorithm, whose complexity order is
to compute exact values. Such an algorithm can be further simplified for moderate sample sizes n, provided that λ is neither close to 
from the left nor close to 
from the right. Sharp estimates, better than other known estimates in the literature, are also provided. The 0s of the second Krawtchouk and Charlier polynomials play a fundamental role.
to compute exact values. Such an algorithm can be further simplified for moderate sample sizes 
from the left nor close to 
from the right. Sharp estimates, better than other known estimates in the literature, are also provided. The 0s of the second Krawtchouk and Charlier polynomials play a fundamental role.