Discretized normal approximation by Stein's method (Q396011)

\textit{L. H. Y. Chen} and \textit{Y. K. Leong} [``From zero-bias to discretized normal approximation'', Personal communication (2010)] obtained a bound on the total variation distance between the sum of integer valued random variables and the discretized normal distribution using the zero-bias coupling approach in Stein's method. In the article under review, a different approach in Stein's method is used to get a bound for the total variation distance between an integer valued random variable and the discretized normal distribution. The utility of the result is illustrated by adapting it to local dependence, exchangeable pairs, and size-biasing and bounding the total variation distance for discretized normal approximations for 2-runs in a sequence of iid Bernoulli random variables, the number of vertices with a given degree in the Erdős-Renyi random graph and the uniform multinomial occupancy model.