Basic probability models for actuarial situations tend to be either continuous or discrete (i.e. not mixed). This calls for either counting something (discrete) or paying something (continuous). In both cases, it is unlikely that the model will need to accommodate negative values. The set of all possible distribution functions is too large to comprehend. Therefore, when searching for a distribution function to use as a model for a random phenomenon, it can be helpful if the field can be narrowed.
In Chapter 3, distributions were distinguished by tail weight. In Section 4.2 distributions are classified based on the complexity of the model. Then, in Chapter 5, a variety of continuous models are developed. Chapters 6 and 7 provide a similar treatment of discrete models.
4.2 The Role of Parameters
In this section, models are characterized by how much information is needed to specify the model. The number of quantities (parameters) needed to do so gives some indication of how complex a model is, in the sense that many items are needed to describe a complex model. Arguments for a simple model include the following:
- With few items required in its specification, it is more likely that each item can be determined more accurately.
- It is more likely to be stable across time and across settings. That is, if the model does well today, it (perhaps with small changes to reflect inflation or similar phenomena) will probably do well tomorrow ...