Common Case Distributions
In the previous two sections, we introduce the most common distributions for modelling the total claim losses. In this section, we are going to discuss several models, which are using for modelling the most useful distributions used in case numbers, such as poisson distribution, negative binomial distribution and binomial distribution.
Poisson Distribution
Characteristics of the Poisson Distribution
If a random variable follows a Poisson distribution, we write
where is the parameter of the distribution.
- PDF:
- CDF:
- Survival function:
Propositions of the Poisson Distribution
- MGF:
- Mean:
- Variance:
::: note Second moment
:::
- Skewness:
::: note Third moment
:::