FA-63373 / Actuarial life tables / Member archive

Life table person-years and expectation: Open interval person-years multiply by the rate · case 03

Expectation at the oldest ages collapses.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Input l (survivors by age, last entry is the open interval) and m_open (per mille central rate of the open interval, <=0 -> 'invalid open rate'). L_x = l_{x+1} + d_x/2, L_open = l_open/m, T_x = sum of L from x, e_x = T_x/l_x rounded to 4 places (None where l_x=0).

Why this case matters

Life-table arithmetic compounds across ages, so one misplaced index or assumption shifts every downstream value.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
table 0	`[4.7647, 3.7755, 2.786, 1.7944, 0.8]`	`[5.2086, 4.2205, 3.2325, 2.2425, 1.25]`	Failed

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