Past exam of the mathematics course of the University of Cambridge 2016 iii Paper 207 4 c Solution Created 2026-10-03 Updated 2026-10-06
For fractional event imputation, let be the fractional event weight assigned to the seventh individual at . Its event contribution at is . It belongs to the risk set at that time precisely for allocations at or later, so its fractional risk set contribution is . This justifies both parts of the hint.
For , the fractional counts at the last three times areEarlier Kaplan–Meier estimator factors still give survival immediately before . ConsequentlyThe three values are , , and , in strictly increasing order. Spreading the censored individual's mass beyond raises the survivor estimate from the immediate-event imputation and moves it toward the original Kaplan–Meier estimator.