An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums

Victor Korolev, Irina Shevtsova

By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\rho (F_n,\Phi )\le \frac{0.335789({\beta }^3+0.425)}{\sqrt{n}}$$ and $$ρ(F_n,Φ)\le \frac…