IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests
A graduation is tested using a chi-square test on 18 age groups. The graduated rates were obtained by fitting a formula with 3 parameters estimated from the data. The test statistic is calculated from the standardised deviations. What are the degrees of freedom to use?
The degrees of freedom are 15. With 18 age groups and 3 parameters estimated from the same data, one subtracts the number of fitted parameters from the number of groups, giving 18 minus 3.
- A18
- B17
- C15Correct
- D14
- 21
Explanation
When parameters are fitted to the same data, degrees of freedom equal the number of groups minus the number of parameters estimated: 18 − 3 = 15. Using 18 ignores the fitting, and 17 deducts one for a total constraint, which is not the rule here.
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