The Markov binomial distribution is approximated by the Poisson distribution with the same mean, by a translated Poisson distribution and by two-parametric Poisson type signed measures. Using an adaptation of Le Cam's operator technique, estimates of accuracy are proved for the total...

Let Sn = X1 + ... + Xn, where X1, ..., Xn are independent Bernoulli random variables. In this paper we present some new results of approximation of the distribution of Sn by a Poisson distribution with respect to the point metric. For this purpose we use the semigroup approach originally...

The distribution of the sum of independent nonidentically distributed Bernoulli random vectors inRkis approximated by a multivariate Poisson distribution. By using a multivariate adaption of Kerstan's (1964,Z. Wahrsch. verw. Gebiete2, 173-179) method, we prove a conjecture of Barbour (1988,J....

We prove optimal constant over root n upper bounds for the maximal probabilities of nth convolution powers of discrete uniform distributions.

We present some new sharp bounds for several distances between the Poisson binomial distribution and the Poisson law with the same mean. It is shown that the constants involved cannot be reduced.