An Expansion for a Discrete Non-Lattice Distribution

Abstract

Much is known about asymptotic expansions for asymptotically normal distributions if these distributions are either absolutely continuous or pure lattice distributions. In this paper we begin an investigation of the discrete but non-lattice case. We tackle one of the simplest examples imaginable and find that curious phenomena occur. Clearly more work is needed.

In memoriam Willem Rutger van Zwet who passed away on July 2, 2020. The article is part of a conference proceedings in 2006 in honor of Peter Bickel