Non integer ages - probabilities
In life tables, we have values for only integer ages and durations. So, we have to separate out fraction of years (i.e. duration less than a year) from full years during total duration. To evaluate fraction of years, we have formulas developed under UDD and CFM assumptions.
Example 1:
4p30.5 : Probability of person aged 30.5 surviving to age 34.5 (duration 4).
Split it as: 30.5 -> 31 (duration 0.5); 31 ->34 (duration 3); 34 -> 34.5 (0.5).
0.5p30.5 * 3p31 * 0.5p34
Example 2:
3.75p30: Probability of person aged 30 surviving to age 33.75 (duration 3.75)
Split it as: 30 -> 33 (duration 3), 33 -> 33.75 (duration 0.75).
3p30 * 0.75p33
Example 3:
2.5p30.5: Probability of person aged 30.5 surviving to age 33 (duration 2.5)
Split it as: 30.5->31 (duration 0.5), 31->33 (duration 2 years).
0.5p30.5 * 2p31
Example 4:
2.75p30.5: Probability of person aged 30.5 surviving to age 33.25 (duration 2.75)
Split it as: 30.5->31 (duration 0.5), 31->33 (duration 2 years), 33-> 33.25 (duration 0.25).
0.5p30.5 * 2p31 & 0.25p33
I guess it is clear now... Pls let me know if not or you have any other questions...
Thanks,
Raj
