The local limit theorem for general weighted sums of Bernoulli random variables

Abstract

The local limit theorem (LLT) is one of the well-known limit theorems which can be used to estimate the probability at a particular point of a random variable. In this paper, we generalize weighted sums which are introduced by Giuliano and Weber and give the LLT with explicit error bounds.

KEYWORDS:

• Local limit theorem
• normal density function
• weighted sums of Bernoulli random variable
• rate of convergence

2020 Mathematics Subject Classification:

• 60F05

Acknowledgments

This work was supported by the Development and Promotion of Science and Technology Talents Project (DPST).