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math.ST updates on arXiv.org

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The density ratio of Poisson binomial versus Poisson distributions
Lutz Duembgen, Jon A. Wellner · 2019-10-08 · via math.ST updates on arXiv.org

Let $b(x)$ be the probability that a sum of independent Bernoulli random variables with parameters $p_1, p_2, p_3, \ldots \in [0,1)$ equals $x$, where $λ:= p_1 + p_2 + p_3 + \cdots$ 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 $λ$.

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