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Estimations in the theorem of the stability of Poisson distribution decompositions

J. J. Mačys

Institute of Physics and Mathematics, Academy of Sciences, Lithuanian SSR

Abstract: Let $\Pi_\lambda$ be a Poisson distribution function and $F=F_1*F_2$ a distribution function such that either in the Lévy metric or in the uniform metric $\rho(F,\Pi_\lambda)\le\varepsilon$.
We show that, there exists a Poisson distribution function $\Pi_{\lambda_1}$ such that
$$ \rho(F_1,\Pi_{\lambda_1})<C(\lambda)\sqrt{\frac{\ln(-\ln\varepsilon)}{(-\ln\varepsilon)}}. $$

 English version: Theory of Probability and its Applications, 1971, 16:2, 215–227

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