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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests

When graduating by a parametric formula, which statement about the balance between smoothness and adherence to data is correct?

Smoothness is judged by inspecting the third differences of graduated rates, which should be small and progress regularly. Adherence to data is tested separately with deviation-based tests. Adding parameters tends to reduce smoothness, and an exact fit copies the crude irregularities.

  1. ASmoothness is usually judged by examining the third differences of the graduated rates, which should be small and progress regularlyCorrect
  2. BAdherence to data is assessed by the smoothness of the third differences
  3. CSmoothness is tested using the signs test on standardised deviations
  4. DIncreasing the number of parameters always improves smoothness
  5. A graduation that fits the crude rates exactly is the smoothest possible

Explanation

Smoothness is checked by looking at differences, commonly third differences, of the graduated rates, which should be small and regular. Fit to data is tested by statistical tests on deviations. More parameters generally reduce smoothness, and an exact fit to crude rates reproduces their irregularity.

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