A STUDY OF PROPERTIES AND REAL-LIFE APPLICATIONS OF NEGATIVE BINOMIAL DISTRIBUTION

This paper delves deep into the characteristics and practical uses of the Negative Binomial Distribution, a discrete probability model extensively utilized across multiple domains such as epidemiology, insurance, and ecology. The exploration commences with a detailed examination of the mathematical attributes of the Negative Binomial Distribution, encompassing its probability mass function, moments, and methodologies for parameter estimation. By conducting this thorough investigation, the objective is to emphasize the importance of the Negative Binomial Distribution in both theoretical and practical scenarios, serving as a valuable reference for scholars and professionals confronted with excessively dispersed count data in diverse fields.This in-depth analysis seeks to shed light on the critical role played by the Negative Binomial Distribution in statistical modeling and empirical studies, offering insights and tools for analyzing data sets characterized by over-dispersion, thus enhancing the understanding and application of this powerful probability distribution.