CONTINUITY OF PROBABILITY MEASURES AND ITS ROLE IN STATISTICAL MODELING

DEMIRI, Edin and A.DEMIRI, Edona and KAMBERI, Lazim (2026) CONTINUITY OF PROBABILITY MEASURES AND ITS ROLE IN STATISTICAL MODELING. In: INTERNATIONAL CONFERENCE “FROM RESEARCH TO APPLICATION”, 20 May, 2026.

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Abstract

This paper examines the notion of continuity in probability measures and its essential function in statistical modelling. In measure-theoretic probability, continuity properties—namely continuity from below and continuity from above—are crucial for examining the asymptotic behavior of sequences of events and random variables. These characteristics guarantee that probability measures exhibit uniformity under monotone limits, establishing a robust foundation for numerous conclusions in probability and statistics. This study establishes the relationship between the continuity of probability measures and fundamental principles in stochastic convergence, such as convergence in probability and almost sure convergence. The paper specifically illustrates the application of continuity arguments to validate the convergence of sequences of random variables, which is fundamental to statistical inference. The role of continuity is also looked at in the context of statistical modelling, with a focus on distribution functions and their right-continuity, as well as on asymptotic results like the Law of Large Numbers. By using specific examples, the paper shows how theoretical continuity properties can be used in real life to make models and estimates in statistics. The findings underscore that the continuity of probability measures is not merely a theoretical construct, but a fundamental principle that underpins the stability and reliability of statistical models. This work offers a cohesive viewpoint that links abstract probability theory to its contemporary applications in statistical analysis.

Item Type: Conference or Workshop Item (Paper)
Subjects: Q Science > QA Mathematics
Depositing User: Unnamed user with email zshi@unite.edu.mk
Date Deposited: 23 Sep 2026 09:27
Last Modified: 23 Sep 2026 09:27
URI: http://eprints.unite.edu.mk/id/eprint/2466

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