When is a proportional hazards model valid for both stock and flow sampled duration data?

Abstract

It is shown that if the flow-sampled total durations and stock-sampled elapsed durations from stationary renewal processes both exhibit proportional hazard rates and are continuous then they belong to the family of survival distributions with linear mean residual functions introduced by Hall and Wellner (1984) [Hall, W.J., Wellner, J.A., 1984. Mean residual life. In: Csörgö, M., Dawson, D.A., Rao, J.N.K., Saleh, A.K.M.E., (Eds.), Proceedings of the International Symposium on Statistics and Related Topics. North Holland, Amsterdam, pp. 169–184].