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...

A correction to an error in a recent paper of Barbour and Brown's is detailed, and a relevant corollary stated.

Computer techniques for scatter-plot smoothing are valuable exploratory analysis tools. However, one must exercise caution when making inferences based on features of the smoothed data. Here, the size and number of observed modes are studied: the asymptotic distributions are determined under the...

Explicit expressions are given for the maximum error between the binomial distribution with parameters n and p and its Poisson approximants, for sufficiently small values of np. Both the error in the cumulative distribution function and that in the probability mass function are given for Poisson...