An Expansion for a Discrete Non-Lattice Distribution

TL;DR

This paper explores the asymptotic expansion properties of a discrete non-lattice distribution, revealing unique phenomena and highlighting the need for further research in this less-studied area.

Contribution

It initiates investigation into the asymptotic behavior of discrete non-lattice distributions, a less understood area compared to lattice or continuous cases.

Findings

Curious phenomena observed in simple discrete non-lattice examples

Highlights gaps in understanding of asymptotic expansions for non-lattice distributions

Calls for further research in this area

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.