Lee Carter
- \(\alpha_x\) captures the age specific pattern of mortality
- \(\kappa_t\) captures the overall mortality trend
- \(\beta_x\) captures the differences in improvements in different ages
\[ \ln(m_{xt})=\alpha_x+\beta_x\kappa_t\]
Cairns-Blake-Dowd
- \(\kappa_t^{(1)}\) captures the intercept, which gives an indication for an overall mortality trend
- \(\kappa_t^{(2)}\) captures the slope, which indicates the rate of change between ages
\[ logit(q_{xt}) = \kappa_t^{(1)} + (x-\bar{x})\kappa_t^{(2)}\]
- This is a linear model, therefore it is best used for older ages as they tend to be linear whereas young ages typically are not.
Age-Period-Cohort
- \(\alpha_x\) captures the age specific pattern of mortality
- \(\kappa_t\) captures the overall mortality trend
- \(\gamma_{t-x}\) captures the cohort effect
\[ \ln(\mu_{xt})=\alpha_x+\kappa_t+\gamma_{t-x}\] 
