for gompertz and makeham model - ch 9 says the shape of the hazard is exponential, but aprl 2012 paper, answer 4, says that the gompertz model has a monotonically increasing or decreasing hazard rate.... I am very confused
Monotonically increasing just means that the slope of the curve is always upwards (mono-, one direction). If you differentiate the Makeham or Gompertz formulas, you'll see they are always greater than zero, so this is always true.
ok, but I would rather write exponential on the exam, as this is what the core reading is saying in several sections of the core reading....
The problem is they are not the same thing - an exponential function is not guaranteed to be monotonic or increasing (consider e^-x^2, for example). A generalised G-M model would cope perfectly well with the data given. So the problem is not that the Gompertz model is exponential, it is that it can't reflect the data accurately, because the observed hazard rate is decreasing.
