Sharp constants in the Poisson approximation (Q5937061)

Using the continuation of the author's arguments in [Bernoulli 5, No. 6, 1021-1034 (1999; Zbl 0951.60040)] and some results by \textit{P. Deheuvels} and \textit{D. Pfeifer} [see, e.g., Ann. Inst. Stat. Math. 40, No. 4, 671-681 (1988; Zbl 0675.60027)], inequalities, optimal in a sense, are established for several distances between the Poisson binomial distribution and the Poisson law with the same mean.