Comparative Analysis of Stochastic Modeling and Computational Efficiency in Poisson Binomial and Annamalai Frameworks

Stochastic modeling of independent Bernoulli trials is a cornerstone of modern statistics. While the standard Binomial distribution assumes a constant probability across trials, the Poisson Binomial Distribution (PBD) provides a more realistic model for non-identical trials. However, its computational complexity limits its scalability in big data environments. This paper evaluates the Annamalai PMF, an innovative combinatorial system, as a high-efficiency framework for calculating these probabilities and modeling waiting times in high-stakes stochastic environments.