Several models of a population survival curve composed of two piecewis
e exponential distributions are developed. In one formulation the haza
rd rate changes at a point that is an unobservable random variable tha
t varies between individuals. The population hazard function may decre
ase with age even when all individuals' hazards are increasing. In a s
econd formulation, the population hazard function is modeled directly.
Several models are fit to the survival history of a cohort of 5751 hi
ghly inbred male Drosophila melanogaster and the British coal mining d
isaster data.