Journal of Population Sciences
Table 1 List of mortality models equations and parameter constraints
From: Mortality forecasting in Colombia from abridged life tables by sex
Mortality model | Formula | Parameter constraints |
|---|---|---|
gnm R-package | ||
Lee-Carter (LC) | logit(qxt)=ax+bxkt | \(\sum _{x} b_{x} = 1\), \(k_{t_{0}} = 0\) |
Lee-Carter with two terms (LC2) | \(\text {logit}(q_{xt})=a_{x} + b_{x}^{1} k_{t}^{1} + b_{x}^{2}k_{t}^{2}\) | \(\sum _{x}b_{x}^{i} = 1, k_{t_{0}}^{i} = 0, i=1,2\) |
Lee-Carter with cohort (LCC) | \(\text {logit}(q_{xt})=a_{x} + b_{x}^{1}k_{t} + b_{x}^{2}\gamma _{c}\) | \(\sum _{x} b_{x}^{i} = 1\), \(k_{t_{0}} = 0\), \(\gamma _{c_{0}} = 0\) |
Age-Period-Cohort(APC) | logit(qxt)=ax+kt+γc | \(k_{t_{0}} = 0\), \(\gamma _{c_{0}} = 0\) |
StMoMo R-package | ||
Renshaw-Haberman (RH) | \(\text {logit}(q_{xt})=a_{x}+b_{x}^{1} k_{t}^{1}+\gamma _{c}\) | \(\sum _{x} b_{x}^{1}=1,\sum _{t} k_{t}=0\), \(\sum _{c} \gamma _{c}=0\) |
Cairns-Blake-Dowd (CBD) | \(\text {logit}(q_{xt})= k_{t}^{1} + (x-\bar {x}) k_{t}^{2}\) | no constraints |
Generalization of CBD (M8) | \(\text {logit}(q_{xt})= k_{t}^{1} +(x - \bar {x})k_{t}^{2}+(x_{c} - x)\gamma _{c}\) | \(\sum _{c} \gamma _{c}=0\) |