IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests
A graduation by a parametric formula with 3 fitted parameters is made to crude rates at 20 ages. The chi-squared test of goodness of fit is applied to the graduated rates. How many degrees of freedom should be used, assuming no grouping of ages is needed?
The chi-squared test has 17 degrees of freedom. The number of age groups, 20, is reduced by the 3 parameters estimated from the data. Using 20 would ignore the fitting, and 19 or 18 would subtract too few parameters.
- A20
- B19
- C18
- D17Correct
- 3
Explanation
Degrees of freedom equal the number of age groups minus the number of fitted parameters: 20 - 3 = 17. Using 20 ignores the fitted parameters. Using 19 subtracts only one, and 18 subtracts two.
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