Lifetime Data Analysis

, Volume 16, Issue 4, pp 571–579 | Cite as

Product-limit estimators of the gap time distribution of a renewal process under different sampling patterns

  • Richard D. Gill
  • Niels Keiding
Open Access


Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes several such situations where simple product limit estimators, though inefficient, may still be useful.


Kaplan–Meier estimator Cox–Vardi estimator Laslett’s line segment problem Nonparametric maximum likelihood Markov process 



This research was partially supported by a grant (RO1CA54706-12) from the National Cancer Institute and by the Danish Natural Sciences Council grant 272-06-0442 “Point process modelling and statistical inference”.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of LeidenLeidenNetherlands
  2. 2.Department of BiostatisticsUniversity of CopenhagenCopenhagenDenmark

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