Signed Poisson approximation: a possible alternative to normal and Poisson laws

Abstract

Signed Poisson approximation is a signed measure, has the structure of the Poisson distribution and can be regarded as a special sort of asymptotic expansion when expansion is in the exponent. For certain lattice distributions signed Poisson approximation combines advantages of both the normal and Poisson approximations. For the generalized binomial distribution estimates with respect to the total variation and Wasserstein distances are obtained. The results are exemplified by Bernoulli decomposable variables.