Yazd University Journal of Statistical Modelling: Theory and Applications 2676-7392 6 2 2025 07 01 A decomposition approach to the asymptotic distribution of the sample variance in discrete models 117 126 4216 10.22034/jsmta.2026.24157.1206 EN Narges Abbasi Department of Statistics‎, ‎Payme Noor University‎, ‎Tehran‎, ‎Iran 0000-0002-2845-1482 Masoud Yarmohammdi Department of Statistics‎, ‎Payme Noor University‎, ‎Tehran‎, ‎Iran 0000-0001-7038-7106 Ali Shadrokh Department of Statistics‎, ‎Payme Noor University‎, ‎Tehran‎, ‎Iran Mahnaz Lashani Department of Statistics‎, ‎Payme Noor University‎, ‎Tehran‎, ‎Iran Journal Article 2025 12 23 Understanding the asymptotic behavior of the sample variance is important in statistical theory and inference. While classical results provide chi-square limiting distributions for continuous populations, discrete random variables often exhibit non-classical behavior, complicating both theoretical analysis and practical applications. In this paper, we propose a decomposition of the sample variance for discrete random variables into two theoretically tractable components, enabling a finer characterization of their stochastic structure. We derive the asymptotic distributions of these components under a specific condition, revealing that certain components converge to chi-square laws - a phenomenon previously observed only in Bernoulli and binomial models with success probability one-half. Extensive Monte Carlo simulations confirm the accuracy of the theoretical approximations and demonstrate their relevance even for moderate sample sizes. These results provide new insights into the interplay between discreteness, variance decomposition, and asymptotic behavior, extending classical chi-square asymptotics to a broader class of discrete models. https://jsm.yazd.ac.ir/article_4216_bf5a73d02687e708630e54ceca4595af.pdf