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- W4311879897 abstract "We say that a random integer variable $X$ is monotone if the modulus of the characteristic function of $X$ is decreasing on $[0,pi]$. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random variables. In this note, we provide estimates for the probability that the sum of independent monotone integer variables attains precisely a specific value. We do not assume that the variables are identically distributed. Our estimates are sharp when the specific value is close to the mean, but they are not useful further out in the tail. By combining with the trick of emph{exponential tilting}, we obtain sharp estimates for the point probabilities in the tail under a slightly stronger assumption on the random integer variables which we call strong monotonicity." @default.
- W4311879897 created "2023-01-02" @default.
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- W4311879897 date "2021-04-08" @default.
- W4311879897 modified "2023-09-29" @default.
- W4311879897 title "On Sums of Monotone Random Integer Variables" @default.
- W4311879897 doi "https://doi.org/10.48550/arxiv.2104.03721" @default.
- W4311879897 hasPublicationYear "2021" @default.
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