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An urn model in the simulation of interval censored failure time data. (English) Zbl 0951.62087
Summary: A self-consistent algorithm was proposed by B.W. Turnbull [J. Am. Stat. Assoc. 69, 169-173 (1974; Zbl 0281.62044)] to estimate the distribution of $X$ on the basis of interval censored data of $X$. An interval censored $X$ means that $X$ is known either to lie inside an interval $\left({X}_{L},{X}_{R}\right]$, or to lie below ${X}_{L}$ or above ${X}_{R}$. The calculation of the estimates is not an easy task. In this article, an urn model is constructed to sample the random intervals and to calculate relevant probabilities. It is proved that using the interval data obtained from the urn model, consistent estimates can be obtained by using the self-consistency algorithm. A simulation example is provided to illustrate the procedure.
##### MSC:
 62N05 Reliability and life testing (survival analysis) 65C60 Computational problems in statistics 62N99 Survival analysis and censored data