Thinning and the Law of Small Numbers
Peter Harremoes, O. Johnson and I. Kontoyiannis
In: ISIT 2007, 24-29 June 2007, France.
The Law of Small Numbers is normally formulated using triangular
arrays. We replace the triangular array by a new mathematical
construction and prove an information theoretic version of the Law
of Small Numbers. By this approach the relation between the Law of
Small Numbers and the information Theoretic version of the Central
Limit Theorem is emphasized. These ideas are also used for the
compound Poisson distributions.