Gaussian Distribution, Poisson Distribution and Exponential Distribution: Theorems and Applications

Abstract

Probabilistic frameworks for representing uncertainty and randomness are indispensable in Statistics and Data Science applications. Among all distributions, some are widely used in healthcare, engineering, and operations management, such as the Gaussian, Poisson and exponential distributions. Based on the three probability distributions, this paper will introduce related research results at present in various areas and several examples of their practical application. It presents the mathematical characteristics and assumptions of each distribution and examines their practical applications. That is, the Gaussian distribution for materials engineering and vessel dynamics, the Poisson process model for call centers and emergency departments, the exponential distribution model for epidemiology and environmental science, etc. It can be concluded from the above results that the shape of a certain probability distribution will vary depending on how it is applied in practice. A thorough understanding of such distributions will assist the construction of statistical models for various science and engineering applications.