Reproducing exhibit 6.14 - Basic Ratemaking

[smilehoe]

4th ed, Pg 111,
There are two tables on the page, the first one listing frequency, severity and pure premium for 12 months ending each quarter year. In the second table, it shows the exponential fit of the data. What formula did the author used to arrive at the values in the second table. Any help? Attached is the excel file with the two tables in it.

[Vorian Atreides]

I doubt that they'll ask for an exponential fit of the data on an Exam question. In practice, an exponential fit is likely to be used, but it's calculation is not all that nice w/o some data transformation.

Replicating the exhibit with your own calculator, what you need is the TI-30X II, and enter the relevant data as if you were going to do a linear fit to the data, except use ln(y) instead of just y.

The regression slope would be the quarterly trend (since the X values are quarterly).

To get an annual trend, you need to take e^{4 times the regression slope} - 1.0 to get the trend value.

I've attached an Excel file to show the details more clearly.

[smilehoe]

Thanks! That was very clear. Especially the excel calculation steps.