CS2 ch3 P.27 Sample Question cEx value

[iamminime]

Hi In ch.3 Section6 (The Poisson model) P.27 Sample Question, about a mortality investigation covering 5-year period with 7500 population
the cEx is taken as 7500*5
However, since cEx is another notation for observed waiting time v = sum(1,n):vi, from my understanding, unless there is no decrement and everyone survives to the end of 5-year period, cEx should be less than 7500*5
I am wondering why cEx is taken as (bi - ai)*n ? instead of sum(1,n):vi ? If it is due to approximation, why cEx is not even E(V)?
Thanks a lot for help!!

 

[Andrew Martin]

Hi Iamminime

In this case, we're told that the population remains approximately constant at 7500 over the course of the 5 years. So the number of people under observation at any point during the period is approximately 7500. Therefore, the total observed time in the alive state is, approximately, 7500 * 5. With the information given in the question, we don't have any more detail to work out a more accurate observed waiting time.

This question is also in the section on the Poisson model. Technically the exposed to risk in the Poisson model is treated as fixed (ie not random) where as V in the two-state model is the random variable of the total amount of time we observe people for in the alive state. Sometimes it is correct that the exposed to risk is fixed (and known prior to the experiment). For example, the question at the bottom of page 24. However, this is not the case for a general mortality investigation and is hence only an approximate approach in such instances.

Hope this helps!

Andy