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• W2110170501 abstract "This paper is devoted to a refinement of Hipp's method in the compound Poisson approximation to the distribution of the sum of independent but not necessarily identically distributed random variables. Approximations by related Kornya-Presman signed measures are also considered. By using alternative proofs, we show that several constants in the upper bounds for the Kolmogorov and the stop-loss distances can be reduced. Concentration functions play an important role in Hipp's method. Therefore, we provide an improvement of the constant in Le~Cam's bound for concentration functions of compound Poisson distributions. But we also follow Hipp's idea to estimate such concentration functions with the help of Kesten's concentration function bound for sums of independent random variables. In fact, under the assumption that the summands are identically distributed, we present a smaller constant in Kesten's bound, the proof of which is based on a slight sharpening of Le Cam's version of the Kolmogorov-Rogozin inequality." @default.
• W2110170501 created "2016-06-24" @default.
• W2110170501 creator A5067237566 @default.
• W2110170501 date "2005-06-01" @default.
• W2110170501 modified "2023-09-30" @default.
• W2110170501 title "On Hipp's compound Poisson approximations via concentration functions" @default.
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• W2110170501 doi "https://doi.org/10.3150/bj/1120591188" @default.
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