Improvements of the nonuniform estimate for convergence of distributions of Poisson randomsums to the normal distribution

The nonuniform estimates for convergence rate in the central limit theorem have been built. Using these structural improvements, it is shown that absolute constant in the nonuniformestimate for convergence rate in the central limit theorem for Poisson random sums is strictly less than similar constant in the nonuniform estimate for convergence rate in the classical central limit theorem and, assuming finite third moment, it does not exceed 22.7707. As a result, nonuniform estimates for convergence rate of the mixed Poisson, particularly, negative binomial, random sums have been built.