Properties of increasing odds rate distributions with a statistical application

• Published in: Journal of statistical planning and inference Vol. 221; pp. 313 - 325
• Main Authors: Lando, Tommaso, Arab, Idir, Oliveira, Paulo Eduardo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2022
• Subjects: Bounds; Hazard rate; Life distributions; Nonparametric test; Order statistics; Stochastic orders; Stochastic orders; Nonparametric test; Hazard rate; Life distributions; Order statistics; Bounds
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2022.05.004

We study the family of distributions characterised by an increasing odds rate (IOR), showing that this provides an alternative interpretation of the “adverse ageing” notion, comparable to the well known increasing hazard rate (IHR) model. We prove some preservation properties of this class under several transformations that are often considered in reliability and life testing problems, including formation of order statistics. Moreover, the IOR assumption enables the derivation of survival bounds and tolerance limits, extending the scope of applicability of some known results, which are based, for instance, on the IHR assumption. Finally, we propose a test for the IOR null hypothesis, establishing its consistency and providing a table of simulated p-values. •We propose the IOR condition as an alternative interpretation of the “adverse ageing” notion.•The IOR is shown to satisfy some closure properties, which are of interest in reliability theory.•Bounds and tolerance limits are obtained assuming the IOR condition, and their application is discussed.•A nonparametric test for IOR is proposed and characterised.