Remarks on estimates in the total-variation metric (Q1592017)

The author considers the approximation of convolutions of lattice distributions by suitably choosen binomial, negative binomial and Poisson distributions replacing the usual normal approximation. This allows to approximate the distributions in terms of the total variation metric in comparison to several weaker metrics considered in the literature. In a second part of the paper, mixtures of distributions are approximated by a convolution of the normal and the Poisson law.