Whereas the UDD approximation assumes that 𝑙𝑥+𝑡 is linear for integral 𝑥 and 0 ≤ 𝑡 ≤ 1, the Balducci hypothesis makes a similar assumption that the inverse of 𝑙𝑥+𝑡 is linear.
|
|
for integral 𝑥 and
0 ≤ 𝑡 ≤ 1 |
Formula 1 |
Based
on this assumption, it follows that
Substituting for 
using Formula
1 gives
Rearranging terms and simplifying leads us to the
widely used assumption for handling fractional-age mortality.
.