Compound Poisson and signed compound Poisson approximations to the Markov binomial law

TL;DR

This paper develops approximation methods for the Markov binomial distribution using compound Poisson and signed compound Poisson measures, providing bounds and asymptotic constants for various norms.

Contribution

It introduces new bounds and asymptotic constants for approximating the Markov binomial law with compound Poisson measures, enhancing accuracy in probabilistic modeling.

Findings

Derived upper and lower bounds for total variation, local, and Wasserstein norms.

Calculated asymptotically sharp constants in a special case.

Applied smoothing properties and characteristic function methods for bounds.

Abstract

Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a special case, asymptotically sharp constants are calculated. For the upper bounds, the smoothing properties of compound Poisson distributions are applied. For the lower bound estimates, the characteristic function method is used.