A local limit theorem for Poisson binomial random variables

We investigate the local limit theorem for Poisson binomial random variables S-n := Sigma(n)(i=1) X-i, where X-1, X-2, ..., X-n 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.

Automated summary

This study focuses on the local limit theorem for Poisson binomial random variables S-n, providing improved explicit bounds for the density of Sn based on Neammanee's ideas.