Frailty distribution among survivors

In a proportional frailty model, Bayes' theorem tilts the original density $g(u)$ among subjects surviving to $t$ toThis survival selection progressively favors smaller frailties.

For unit-rate exponential distribution frailty, the population survival and hazard in a proportional frailty model areThe surviving frailty distribution is exponential with rate $1+H_0(t)$.