On the decomposition of lattice distributions into convolutions of Poisson signed measures

This work provides some results on the convolutions of a special kind of signed measure known as the Poisson signed measure. We show a simple way of obtaining asymptotic decompositions into convolutions of Poisson signed measure that is appropriate for a broad range of lattice distributions. The work demonstrates the analogy between such decompositions and the classic Gram–Charlier decompositions of type $A$ and $B$, and the Edgeworth-Cramer series.