The density ratio of generalized binomial versus Poisson distributions

10/08/2019

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by   Lutz Duembgen, et al.

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Let b(x) be the probability that a sum of independent Bernoulli random variables with parameters p_1, p_2, p_3, ...∈ [0,1) equals x, where λ := p_1 + p_2 + p_3 + ... is finite. We prove two inequalities for the maximal ratio b(x)/π_λ(x), where π_λ is the weight function of the Poisson distribution with parameter λ.