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

A mortality actuary graduates crude rates by fitting a parametric formula such as Makeham's law. Which statement best describes a feature of parametric graduation compared with graduation by reference to a standard table?

Parametric graduation summarises the pattern of mortality by age in a small number of fitted parameters, for example in Makeham's formula. It needs no standard table, gives smooth rates, can help at sparse ages, and gives no guarantee of passing goodness-of-fit tests.

  1. AIt requires an existing published standard table to be available
  2. BIt summarises the age pattern of mortality in a small number of fitted parametersCorrect
  3. CIt leaves the graduated rates equal to the crude rates at every age
  4. DIt cannot be used to extrapolate to ages with sparse data
  5. It guarantees that the graduated rates will pass the chi-squared test

Explanation

Parametric graduation fits a formula, such as Makeham's, whose few parameters are estimated from the data, giving smooth rates. It needs no standard table. It can help extrapolate to sparse ages, and it does not guarantee that any test is passed.

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