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

+2 votes
1,639 views
asked May 28, 2017

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

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

Are these not equivalent?

Thanks

## 1 Answer

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

Best answer

Hi

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.