### Effective dimension

#### (Feb 19, 2014)

Actuaries often need to smooth mortality rates.  Gompertz (1825) smoothed mortality rates by age and his famous law was a landmark in this area.  Figure 1 shows the Gompertz model fitted to CMI assured lives data for ages 20-90 in the year 2002. The Gompertz Law usually breaks down below about age 40 and a more general smooth curve would be appropriate.  However, a more general smooth curve would obviously require more parameters than the two for the simple Gompertz model.

Figure 1.  Crude mortality rates (black dots) with fitted Gompertz line (solid red) on a logarithmic scale.

When we switch to a forecasting scenario, Figure 2 shows both a straight line and a parabola fitted to years 1947-2002 for age 70.  Clearly,…