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
|
