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Abstract
The purpose of this paper is to cover the history and the application of actuarial science, the survival models used, and the applications of these models. This paper will involve a brief history of the probability and statistics that lead up to the actuarial field, the history of actuarial science itself, and the models that are used. The models that are covered are the uniform distribution, the exponential distribution, the Gompertz-Makeham distribution, and the log-normal distribution. These are the core models that are used in actuarial science, and they help in understanding the life tables that are used heavily in this field. These life tables have led many developments in actuarial science and the models described can generate different life tables based on the application of them, as well as becoming the building blocks of many other medicinal and biological fields as the need for data on life-times of not just humans, but biological life as a whole, grows with time.