A New Method for Estimating Life Distributions from Incomplete Data

John Kitchin, Naftali A. Langberg, Frank Proschan

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a new estimator for a continuous life distribution from incomplete data, the Piecewise Exponential Estimator (PEXE). We show that the PEXE is strongly consistent under a mild restriction on the distribution of the censoring random variables (possibly non-identical and non-continuous). Then we consider the Product Limit Estimator (PLE), introduced by Kaplan and Meier (1958). We prove the strong consistency of the PLE under a mild regularity condition on the distributions of the censoring random variables. This result extends previous ones obtained by various researchers. Finally we compare the new PEXE and traditional PLE.

Original languageEnglish
Pages (from-to)241-256
Number of pages16
JournalStatistics and Risk Modeling
Volume1
Issue number3
DOIs
StatePublished - Mar 1983

Bibliographical note

Funding Information:
Research supported by the Air Force Office of Scientific Research, AFSC,

Keywords

  • estimating life distributions censoring random variables strong consistency
  • Piecewise Exponential Estimator Product Limit Estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty

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