Modeling the severity of losses is an important part of actuarial modeling (severity is the dollar value per claim). One approach is to employ parametric models in the modeling process. For example, the process may involve using claims data to estimate the parameters of the fitted model and then using the fitted model for estimation of future claim costs. A companion blog called Topics in Actuarial Modeling introduces a catalog of parametric severity models (the catalog is found here).

The catalog lists the models according to their mathematical properties (e.g. how they are derived and how they are related to the gamma distribution). The models have been discussed quite extensively in the blog for Topics in Actuarial Modeling. The catalog puts all the models in one place so to speak. It has the links to the blog posts that describe the models. Just click on a link if anyone is interested in knowing more about a particular parametric model. The parametric models in the catalog include the following:

- Gamma distribution
- Erlang distribution
- Exponential distribution
- Chi-squared distribution
- Hypo-Exponential distribution
- Hyper-Exponential distribution
- Lognormal distribution
- Weibull distribution
- Transformed exponential distribution
- Inverse exponential distribution
- Inverse transformed exponential distribution
- Transformed gamma distribution
- Inverse gamma distribution
- Inverse transformed gamma distribution
- Transformed Pareto distribution = Burr distribution
- Inverse Pareto distribution
- Inverse transformed Pareto distribution = Inverse Burr distribution
- Paralogistic distribution
- Inverse paralogistic distribution
- Pareto distribution
- Generalized Pareto distribution
- Loglogistic distribution
- Student t distribution
- Beta distribution
- Generalized beta distribution

This list is by no means comprehensive or exhaustive. It should be a good resource to begin the modeling process (or the study of the actuarial modeling process). In fact, the modeling process is part of the exam syllabus of the Society of Actuaries. The catalog of models is found here.

actuarial modeling

parametric severity models

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2017 – Dan Ma