Abstract: Uniform stochastic ordering (USO), also known as hazard rate or failure rate ordering, has garnered significant interest across various applications. In this study, we present nonparametric approaches for comparing distributions within the framework of USO using the ordinal dominance curve. Our study consists of three main components. The first one offers new tests for equality among multiple distributions under USO assumptions. Secondly, we provide goodness-of-fit tests to investigate whether multiple distributions adhere to USO. Lastly, we identify distributions that exhibit significant statistical differences within the context of USO. We provide asymptotic properties and supporting numerical evidence for our proposed methods. To exemplify the application of our inferential techniques, we focus on a biomarker, microfibrillar-associated protein 4, and assess its potential for diagnosing fibrosis stages in hepatitis C patients.

Key words and phrases: Bonferroni correction, Brownian bridge, hazard rate ordering, order-restricted inference, ordinal dominance curve.