On bounds in Poisson approximation for distributions of independent negative-binomial distributed random variables
Abstract
Using the Stein–Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.
A nonuniform bound for the approximation of Poisson binomial byPoisson distribution
It is well known that Poisson binomial distribution 
can be approximated by Poisson distribution. In this paper, we 
give a nonuniform bound of this 
approximation by using Stein-Chen method.
On the Rate of Multivariate Poisson Convergence
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. Appl. Probab.25A, 175?184) on removing a log-term in the upper bound of the total variation distance. Second-order approximations are included.