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 Incoming links: Survival selection in a heterogeneous population

Decreasing population hazard under constant individual hazards 2026-10-14

For a nonnegative random constant individual hazard

Λ

, write

M_{k} (t) = E [Λ^{k} e^{- Λ t}]

. The population survivor function is

M_{0}

and its hazard is

M_{1} / M_{0}

. Under the integrability needed to differentiate,

M_{k}^{'} = - M_{k + 1}

, so

\overline{h}^{'} = \frac{- M _{2} M _{0} + M _{1}^{2}}{M _{0}^{2}} = - Var (Λ ∣ T > t) .

The conditional distribution is weighted by

e^{- Λ t}

. This proves decreasing population hazard without any decrease in individual hazards and explains survival selection in a heterogeneous population.

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