Nonparametric inference about increasing odds rate distributions

Abstract

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 to detect deviations from the IOR property and establish their consistency. The performance of these tests is also evaluated through simulations.

Keywords:

• Hazard rate
• heavy tails
• nonparametric test
• odds

MSC 2010:

• 62G05
• 62G10
• 62N05

Acknowledgements

We are grateful to the two anonymous referees for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

T.L. was supported by the Italian funds ex MURST 60% 2021, by the Czech Science Foundation (GACR) under project 20-16764S and VŠB-TU Ostrava under the SGS project SP2021/15. I.A. and P.E.O. were partially supported by the Centre for Mathematics of the University of Coimbra UID/MAT/00324/2020, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.