Joint-life status and Gompertz’s law

Abstract In this paper we prove that in a survivorship group, the force of mortality of the group must follow Gompertz’s law provided that, for the joint-life status of every two lives, one can find a single-life status whose time-until-death’s distribution equals that of the joint-life status. Therefore, the assumption that the force of mortality follows Gompertz’s law is the necessary and sufficient criterion to guarantee that every joint-life status’ survival pattern can be replaced by a single-life status’ in the group.