  To improve nonparametric estimates of lifetime distributions, we propose
using the increasing odds rate (IOR) model as an alternative to other popular,
but more restrictive, ``adverse ageing'' models, such as the increasing hazard
rate one. This extends the scope of applicability of some methods for
statistical inference under order restrictions, since the IOR model is
compatible with heavy-tailed and bathtub distributions. We study a strongly
uniformly consistent estimator of the cumulative distribution function of
interest under the IOR constraint. Numerical evidence shows that this estimator
often outperforms the classic empirical distribution function when the
underlying model does belong to the IOR family. We also study two different
tests, aimed at detecting deviations from the IOR property, and we establish
their consistency. The performance of these tests is also evaluated through
simulations.
