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Biometrika 1988 75(2):319-324; doi:10.1093/biomet/75.2.319
© 1988 by Biometrika Trust
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Estimation of the survival function with increasing failure rate based on left truncated and right censored data

WEI-YANN TSAI

Division of Biostatistics, Columbia University New York, New York 10032, U.S.A.

The maximum conditional likelihood estimator of the survival function with increasing hazard rate is derived, based on left truncated and right censored data. This estimator always exists, whereas the fully nonparametric conditional maximum likelihood estimator may not exist. A strong consistency theorem is established based on the total time on test transformation.

Key Words: Censoring • Increasing failure rate • Maximum conditional likelihood • Strong consistency • Total time on test • Truncation


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