TITLE

EXACT VALUES AND SHARP ESTIMATES FOR THE TOTAL VARIATION DISTANCE BETWEEN BINOMIAL AND POISSON DISTRIBUTIONS

AUTHOR(S)
ADELL, JOSÉ A.; ANOZ, JOSÉ M.; LEKUONA, ALBERTO
PUB. DATE
December 2008
SOURCE
Advances in Applied Probability;Dec2008, Vol. 40 Issue 4, p1033
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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 √λ, to compute exact values. Such an algorithm can be further simplified for moderate sample sizes n, provided that λ is neither close to l + √l, l = 1, 2, … , from the left nor close to m-√m, m = 2, 3, … , 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.
ACCESSION #
36124396

 

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