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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYThe competing risks set-up is considered where an individual is subject to failure due to two independent competing risks. The available data consist of observed times to failure and the causes of failure. On the basis of this information, distribution-free tests are proposed for testing the equality of the two failure distributions against location, scale and general stochastic ordering alternatives. Locally most powerful rank tests are derived and a generalization of the Wilcoxon test has been proposed. Exact critical points are provided for the newly proposed tests, and Pitman efficiency comparisons made.Some key words: Asymptotic relative efficiency; Locally most powerful rank test; Rank test; U-statistic.

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SummaryHere we consider a competing risks model where the two risks of interest are not independent. The dependence is due to the additive effect of an independent contaminating risk on two initially independent risks. The problem is identifiable when the three risks follow independent exponential distributions and also when the two initial risks follow proportional hazards model. Procedures are suggested for estimation and testing hypotheses regarding the parameters of the three exponentials in the first case and the constant of proportionality in the second case, when the information available consists of the times to death and the causes of death of the individuals.

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