Shevtsova, I. G. On the accuracy of the normal approximation to compound Poisson distributions. (English) Zbl 1298.60033 Theory Probab. Appl. 58, No. 1, 138-158 (2014); translation from Teor. Veroyatn. Primen. 58, No. 1, 152-176 (2013). Let \(X_{1},X_{2},\dots\) be independent identically distributed random variables with a common distribution function \(F\). Let \(N_{\lambda}\) be a random variable with the Poisson distribution with parameter \(\lambda>0\) . Let \(N_{\lambda}\) be independent of the sequence \(X_{1},X_{2},\dots\) for each \(\lambda>0\). The distribution \(F_{\lambda}\) of the random variable \(S_{\lambda}=X_{1}+\cdot\cdot\cdot+X_{N_{\lambda}}\) is called a compound Poisson distribution. The asymptotic normality of compound Poisson distributions means that the uniform distance \[ \Delta_{\lambda}\left( F\right) =\sup_{x}\left| F_{\lambda}\left( x\right) -\Phi\left( x\right) \right| , \] where \(\Phi\) is the standard normal distribution function, tends to zero as \(\lambda\) grows.Under some assumptions on \(F\), the author studies the accuracy of the normal approximation of compound Poisson distributions: \(\Delta_{\lambda}\left( F\right) \rightarrow0\) as \(\lambda\rightarrow\infty\). Reviewer: Wiesław Dziubdziela (Miedziana Gora) Cited in 3 Documents MSC: 60F05 Central limit and other weak theorems 60F99 Limit theorems in probability theory Keywords:Poisson random sum; central limit theorem; convergence rate estimate; normal approximation; Berry-Esseen inequality; asymptotically exact constant PDF BibTeX XML Cite \textit{I. G. Shevtsova}, Theory Probab. Appl. 58, No. 1, 138--158 (2014; Zbl 1298.60033); translation from Teor. Veroyatn. Primen. 58, No. 1, 152--176 (2013) Full Text: DOI