Improvements of Poisson approximation for n-dimensional unit cube random graph

Abstract

This paper uses the Stein-Chen method to obtain uniform and non-uniform bounds in the Poisson approximation for the n-dimensional unit cube random graph. These bounds are re-established under the restriction of Poisson mean λ = 1. One bound is for the distance of two probability functions and the two other bounds are for the distance of two cumulative distribution functions. Furthermore, the last two bounds of this study are sharper than those proposed in Teerapabolarn (2014).

Keywords

• poisson approximation
• n-dimensional unit cube random graph
• stein-chen method