A Charlier-Parseval approach to Poisson approximation and its applications
Vytas Zacharovas, Hsien-Kuei Hwang
TL;DR
This paper introduces a novel method for Poisson approximation using Charlier polynomials and Parseval's identity, leading to improved bounds and a comprehensive survey of related results.
Contribution
It presents a new approach based on Charlier polynomials and Parseval's identity, providing more effective bounds for Poisson approximation problems.
Findings
New bounds for Poisson approximation problems
Application of Charlier polynomials and Parseval's identity
Survey of diverse Poisson approximation results
Abstract
A new approach to Poisson approximation is proposed. The basic idea is very simple and based on properties of the Charlier polynomials and the Parseval identity. Such an approach quickly leads to new effective bounds for several Poisson approximation problems. A selected survey on diverse Poisson approximation results is also given.
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Taxonomy
TopicsMathematical functions and polynomials · Mathematical Approximation and Integration · Random Matrices and Applications