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

A graduation test compares crude and graduated mortality rates. A very large positive value of the sum of the signs, with most deviations (actual minus expected deaths) positive across a long run of ages, indicates that the graduated rates:

The graduated rates are too low. Mostly positive deviations mean actual deaths exceed those expected under the graduation, so the graduated rates understate mortality, and the signs test would show bias.

  1. Aare too high, overstating mortality over that range
  2. Bare too low, understating mortality over that rangeCorrect
  3. Care too smooth, but unbiased overall
  4. Dhave been fitted using too many parameters
  5. are consistent with the crude rates

Explanation

Positive deviations mean actual deaths exceed expected deaths computed from the graduated rates. The graduated rates therefore understate mortality over that range. The signs test would reject the graduation for bias.

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