Why does Pele get an initial exposed to risk of 365 days when the central exposed for risk at age 34 was 48 days? Alternative solution is 48 + 0.5(1) which is very different to 365
The formula for the initial exposed to risk is given on page 8 of Chapter 10. We take the value of the central exposed to risk, and then for each death, we add on the time period 1-ti. This is the time period from the date of death of the life to the end of the year of age. So in this case we need to add on the rest of the year to get the initial exposed to risk from the central exposed to risk. (The reasoning behind this formula for the initial exposed to risk - ie WHY we do this - is beyond the scope of CT4.) The alternative is an approximation based on the assumption that deaths occur on average half way through each year. This is clearly a poor approximation in this case as the life dies only 48 days through the year. It is a better approximation in bigger samples where there are many deaths observed in the year of age.
