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• W3100253441 abstract "Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the distribution of the sum $sum_{i=1}^nX_i$ and an appropriate Poisson or compound Poisson distribution. These bounds include a factor which depends on the smoothness of the approximating Poisson or compound Poisson distribution. This smoothness factor is of order $mathrm{O}(sigma ^{-2})$, according to a heuristic argument, where $sigma ^2$ denotes the variance of the approximating distribution. In this way, we offer sharp error estimates for a large range of values of the parameters. Finally, specific examples concerning appearances of rare runs in sequences of Bernoulli trials are presented by way of illustration." @default.
• W3100253441 created "2020-11-23" @default.
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• W3100253441 date "2010-05-01" @default.
• W3100253441 modified "2023-09-25" @default.
• W3100253441 title "A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables" @default.
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• W3100253441 doi "https://doi.org/10.3150/09-bej201" @default.
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