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What is the difference between central rate of mortality and force of mortality? They seem to have the same formula

+2 votes
asked May 28, 2017 in BUS 3018F - Models by 25b14c23 (400 points)

The formula for the central rate of mortality is given as :image

and the formula for the force of mortality is given as :image

Are these not equivalent?


1 Answer

+3 votes
answered May 28, 2017 by asilmotala (2,610 points)
Best answer


So you actually ask an interesting question, and what it comes down to is the difference between what something represents does not necessarily imply a difference in their estimators.

So the force of mortality, \(\mu_x \), represents the instantaneous rate of transition from alive to dead (i.e. the probability of dying right now given you are alive), and is estimated from data as \(\frac{d_x}{E^c_x}\).

On the other hand, the central rate of mortality, \(m_x \), represents the "average deaths" per person aged x (look back at the slides in the first section). It is calculated by \(\frac{number of deaths}{time spent alive and at risk} \).

Thus the estimates of these two happen to be the same, yet they represent completely different concepts. Furthermore, the rate of mortality is a constant for an age x, whereas the true force of mortality is usually a function of t for an age x.