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

Which of the following is a recognised weakness of the chi-square test of a graduation that the runs test or serial correlations test is designed to address?

The chi-square test can miss clumping of deviations: small deviations that share the same sign over long runs of ages can still give an acceptable statistic, so signs, runs or serial correlation tests are used alongside it.

  1. AIt cannot detect a graduation that is too smooth
  2. BIt may fail to detect a graduation whose deviations are all small but are systematically of the same sign over long stretches of agesCorrect
  3. CIt requires the graduated rates to equal the crude rates
  4. DIt can only be used for graduations by reference to a standard table
  5. It ignores the number of ages in the table

Explanation

The chi-square test looks at the size of deviations but not their pattern, so a graduation with small deviations of consistent sign can pass. Signs, runs and serial correlation tests detect such clumping of deviations.

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