Nonparametric inference about increasing odds rate distributions

TL;DR

This paper introduces a nonparametric inference method for lifetime distributions using the increasing odds rate (IOR) model, which is more flexible than traditional models and suitable for heavy-tailed distributions.

Contribution

It proposes a strongly consistent estimator under the IOR constraint and develops two tests for detecting deviations from the IOR property, with demonstrated effectiveness.

Findings

The estimator often outperforms the empirical distribution function when the IOR model holds.

The proposed tests are consistent and effective in simulations.

The IOR model extends applicability to heavy-tailed and bathtub 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, aimed at detecting deviations from the IOR property, and we establish their consistency. The performance of these tests is also evaluated through simulations.