NEGATIVE BINOMIAL DISTRIBUTION
Keywords:
negative binomial distribution, branching processes, stochastic processes, Poisson and Gamma distributions, count data modeling, risk modeling, parameter estimation, queueing theory.Abstract
This paper provides a concise yet rigorous exposition of the negative binomial distribution, which generalizes the classical binomial model to accommodate overdispersion in count data. Owing to its derivation as a Poisson-Gamma mixture, the distribution possesses remarkable flexibility in modeling heterogeneous stochastic phenomena. It naturally arises in branching processes, risk theory, queueing systems, and waiting time analysis.
We outline its key probabilistic properties, discuss parameter estimation techniques and examine its asymptotic characteristics. The distribution's theoretical richness and practical relevance make it an indispensable tool in stochastic modeling across various applied domains such as epidemiology, actuarial science, and reliability engineering.
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