Mortality rate models
| Model | Mechanism / Formula | Where It Succeeds | Where It Fails |
| Gompertz (1825) | Assumes mortality risk accelerates exponentially with age:<br>μ(x)=μ0ebxμ(x)=μ0ebx<br> | Fits adult mortality (ages 30–80 in humans) exceptionally well | Fails at both ends of life: Cannot model high infant/juvenile mortality, and misses the speculated old-age plateau ( Vaupel et al.) |
| Standard Weibull (1951) | Assumes failure occurs like physical wear-and-tear via a power law:<br>μ(x)∝xβ−1μ(x)∝xβ−1<br>. Survival is<br>S(x)=exp(−(x/α)β)S(x)=exp(−(x/α)β)<br>. | Great for populations where risk steadily rises (<br>β>1β>1<br>) or steadily falls (<br>β<1β<1<br>) | <br>ββ<br>is fixed as a constant: A single constant<br>ββ<br>cannot model a creature that has high infant mortality and adult survival and old-age senescence in the same lifetime |
| Weon & Je | S(u)=exp(−uβ(u)) |