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Poisson approximation in $χ^2$ distance by Chen-Stein approach
Vytas Zacharovas · 2021-09-11 · via math.PR updates on arXiv.org

The main purpose of the paper is to investigate the possibility of applying Chen-Stein approach to estimate the $χ^2$ distance between Poisson distribution and a sum of independent indicators. Earlier results concerning $χ^2$ 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 $χ^2$ distance that are of comparable strength to the earlier estimates obtained by other approaches.

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