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

In the context of graduating mortality rates, which statement best describes the main reason for graduating a set of crude estimates of q_x?

Graduation smooths random sampling errors in crude mortality estimates, using the belief that true rates change smoothly with age, while keeping the graduated rates reasonably close to the observed data. It does not eliminate error entirely, nor reproduce crude rates exactly.

  1. ATo remove all random sampling variation so that the graduated rates equal the true rates exactly
  2. BTo make the graduated rates agree exactly with the observed crude rates at every age
  3. CTo smooth out random sampling errors, using the expectation that true mortality rates progress smoothly with age, while keeping the graduated rates close to the dataCorrect
  4. DTo increase the variance of the estimates so that tests of fit become more powerful
  5. To ensure the graduated rates are always lower than the crude rates at older ages

Explanation

Crude rates carry sampling error, and true mortality is expected to vary smoothly with age. Graduation smooths the crude rates while staying adherent to the data. It cannot remove error completely, so the first option overstates what is achieved. Exact agreement would keep the roughness.

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