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.
Approximation Results for Sums of Independent Random Variables.
In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation distance. The error bounds obtained are either comparable to or improvement over the existing bounds available in the literature. Also, we give an application to the waiting time distribution of 2-runs.
Points of strong summability of Fourier series
In this paper we present a new solution of Hardy and Littlewood's problem concerning strong summability of Fourier series; we also present a property of points of strong summability.