A statistical distribution with an unbounded hazard function and its application to a theory from demography

We introduce a statistical distribution with hazard function mu(t) proportional to (psi-t)beta-1 for 0 less than or equal to t less than psi and shape parameter beta satisfying 0 less than beta less than 1. This hazard function is suggested by a theory of aging in demography. We discuss properties of this distribution and maximum likelihood estimates of its parameters. Mixture distributions are considered to account for pooling across dissimilar populations. This model is compared with the Gompertz and generalized Pareto distributions and used to estimate a finite limit on human lifespan based on the survival of a group of female centenarians.