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The Probability That the Largest Observation Is Censored

R. A. Maller and S. Zhou
Journal of Applied Probability
Vol. 30, No. 3 (Sep., 1993), pp. 602-615
DOI: 10.2307/3214769
Stable URL: http://www.jstor.org/stable/3214769
Page Count: 14
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Probability That the Largest Observation Is Censored
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Abstract

Suppose n possibly censored survival times are observed under an independent censoring model, in which the observed times are generated as the minimum of independent positive failure and censor random variables. A practical difficulty arises when the largest observation is censored since then the usual non-parametric estimator of the distribution of the survival time is improper. We calculate the probability that this occurs and give necessary and sufficient conditions for this probability to converge to 0 as n→∞. As an application, we show that if this probability is 0, asymptotically, then a consistent estimator for the mean failure time can be found. An almost sure version of the problem is also considered.

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