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Research articles

ScienceAsia 47 (2021): 111-116 |doi: 10.2306/scienceasia1513-1874.2021.006


A local limit theorem for Poisson binomial random variables


Tatpon Siripraparata, Kritsana Neammaneea,b,*

 
ABSTRACT:     We investigate the local limit theorem for Poisson binomial random variables Sn := Pn i=1 Xi, where X1, X2,. .. , Xn are independent Bernoulli random variables. Using the idea from Neammanee [Int J Math Math Sci 5 (2005):717?728], we derive improved explicit bounds for the density of Sn.

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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 10400 Thailand

* Corresponding author, E-mail: Kritsana.N@chula.ac.th

Received 11 Jun 2020, Accepted 18 Nov 2020