This article proposes inference procedures for distribution regression models in duration analysis using randomly right-censored data. This generalizes classical duration models by allowing situations where explanatory variables' marginal effects freely vary with duration time. The article discusses applications to testing uniform restrictions on the varying coefficients, inferences on average marginal effects, and others involving conditional distribution estimates. Finite sample properties of the proposed method are studied by means of Monte Carlo experiments. Finally, we apply our proposal to study the effects of unemployment benefits on unemployment duration.