Survival model (Mux)

[Rahul]

Core Reading says:
The intuitive way of thinking of the force of mortality is in terms of the expected number of deaths in a very large population. The expected number of deaths during a short time interval of length h years in a very large population consisting of n individuals aged exactly x is n*h*mu(x).

Could you please help me to understand what do we mean by h years in the above?
It would be really helpful if you could give me numerical example and interpretation in words of the above equation(N*h*mu(x)).

Thank you in advance.

 

[Andrew Martin]

Hi Rahul

Say mu(x) = 0.007377, n = 100,000 and we are considering the period of 1 day. Assuming 365 days in a year, then h is 1/365. The number of deaths we would expect during this one day is (approximately) 0.007377 * 100,000 * 1/365 = 2.021. So we'd expect about 2 people to die.

Note that although it appears to be stated as an exact result, this is an approximation for any actual value of h > 0. The definition of mu(x) is based on this idea but it is calculated as when we take the limit as h goes to 0.

Hope this helps.