Poisson approximation in χ² distance by Chen-Stein approach

2021/09/10 by Vytas Zacharovas, Zacharovas, Vytas
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2109.04982

openalex publication_date 2021/09/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

The main purpose of the paper is to investigate the possibility of applying Chen-Stein approach to estimate the χ² distance between Poisson distribution and a sum of independent indicators. Earlier results concerning χ² distance between above mentioned distributions either used analytical approach heavily based on the analysis of the generating functions or on rather lengthy and complicated elementary calculations. Applying Chen-Stein approach we succeed in providing a very quick proof of upper bounds for χ² distance that are of comparable strength to the earlier estimates obtained by other approaches.

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