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Research articles

ScienceAsia 50 (2024):ID 2024034 1-6 |doi: 10.2306/scienceasia1513-1874.2024.034

A refinement of a local limit theorem for a Poisson binomial random variable

Suporn Jongpreechaharna,*, Chananwit Sridusitluka, Kritsana Neammaneea,b

ABSTRACT:     In this paper, a local limit theorem is proposed for a Poisson binomial random variable with a normal random variable as a limit distribution. Our result improves the convergence rate of previous research from 1/?2 to 1/?3 , where ? 2 is a variance of the Poisson binomial random variable. The order of an error bound is equal to the best rate of convergence in the case of a symmetric binomial random variable. The methods for this work are the characteristic function and the correction term approaches.

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a Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330 Thailand
b Centre of Excellence in Mathematics, Commission on Higher Education, Bangkok, Thailand

* Corresponding author, E-mail: suporn.j@chula.ac.th

Received 11 Sep 2022, Accepted 20 Feb 2024