  There is sustained and widespread interest in understanding the limit, if
any, to the human lifespan. Apart from its intrinsic and biological interest,
changes in survival in old age have implications for the sustainability of
social security systems. A central question is whether the endpoint of the
underlying lifetime distribution is finite. Recent analyses of data on the
oldest human lifetimes have led to competing claims about survival and to some
controversy, due in part to incorrect statistical analysis. This paper
discusses the particularities of such data, outlines correct ways of handling
them and presents suitable models and methods for their analysis. We provide a
critical assessment of some earlier work and illustrate the ideas through
reanalysis of semi-supercentenarian lifetime data. Our analysis suggests that
remaining life-length after age 109 is exponentially distributed, and that any
upper limit lies well beyond the highest lifetime yet reliably recorded. Lower
limits to 95% confidence intervals for the human lifespan are around 130 years,
and point estimates typically indicate no upper limit at all.
