Final answer:
The Normal and Poisson distributions are commonly used in actuarial science to model claim sizes, with the former most suited for a wide range of continuous variables and the latter for counting the number of events in a fixed period.
Step-by-step explanation:
In the field of actuarial science, two particularly significant probability distributions employed for modeling individual claim size data are the Normal Distribution and the Poisson Distribution.
Normal Distribution
The Normal Distribution is a continuous probability distribution that is bell-shaped and most prominently characterized by its mean (μ) and standard deviation (σ). It is the go-to distribution due to its mathematical properties and natural occurrence in various phenomena. It is also favored in actuarial calculations because it can be applied to model a wide range of random variables, and the Central Limit Theorem ensures that means of sample distributions tend to be normally distributed regardless of the underlying distribution.
Poisson Distribution
On the other hand, the Poisson Distribution is a discrete probability distribution that is used to model the count of events that occur randomly over a fixed interval of time or space. Key characteristics include its mean (λ) and its ability to model rare events, making it suited for estimating the number of claims within a given period. Unlike the Normal Distribution, the Poisson is typically used when the focus is on counting occurrences rather than measuring things, which is often the case in insurance claim data.