Neutrosophic geometric distribution: Data generation under uncertainty and practical applications

This paper introduces the geometric distribution in the context of neutrosophic statistics. The research outlines the essential properties of this new distribution and introduces novel algorithms for generating imprecise geometric data. The study explores the practical applications of this distribution in the industry, highlighting differences in data generated under deterministic and indeterminate conditions using detailed tables, simulation studies, and real - world applications. The results indicate that the level of uncertainty has a substantial impact on data generation from the geometric distribution. These findings suggest updating classical statistical algorithms to better handle the generation of imprecise data. Therefore, decision - makers should exercise caution when using data from the geometric distribution in uncertain environments.