Exposure

The reason for entering exposure is to separate it from other sources of variation in frequency, such as trend, seasonality, and coverage changes.

**Exposure is
implemented by a means of "pro rata" in the Simulator as
followed**:

To illustrate how exposure affects the conversion of annual frequency,

let’s assume that the user
inputs a **Poisson**
“annual frequency”
with lambda= 4800,

and that the exposure vector is <2,1,1,2,1,1,2,1,1,2,1,1>.

The total of the vector elements above is 16.

In this example, we will ignore the trend, seasonality, etc, other factors. Then the "monthly frequency" parameter lambda for months 1, 4, 7, and 10 would be 4800 x (2/16) = 600, and the parameter for the other months would be 300. By this way, the resulting parameter lambda for the annual number of claims would then be the original input value 4800.

The entire discussion above
carries through for the **negative binomial**
distribution also. For this distribution, the “size”
parameter would be treated in a manner analogous to lambda
for the Poisson distribution.