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

A mortality investigation for ages 40 to 70 is graduated by fitting a Gompertz-type formula, mu_x = exp(a + b x), to the crude rates by maximum likelihood. Which description best classifies this method?

This is parametric graduation. A mathematical formula with a small number of parameters, here a Gompertz-type form, is fitted to the crude rates by maximum likelihood. No existing table is adjusted and no curve is drawn by eye or smoothed locally.

  1. AGraduation by reference to a standard table
  2. BParametric graduationCorrect
  3. CGraduation by graphical methods
  4. DNon-parametric graduation using kernel smoothing
  5. Graduation by linear transformation of a published table

Explanation

Fitting a mathematical formula with a few parameters estimated from the data is parametric graduation. Standard-table methods use an existing table with adjusted parameters, which is different. Graphical methods fit a curve by eye, and kernel smoothing has no fixed formula.

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