A New Method for Estimating Life Distributions from Incomplete Data

John Kitchin; Naftali A. Langberg; Frank Proschan

doi:10.1524/strm.1983.1.3.241

A New Method for Estimating Life Distributions from Incomplete Data

John Kitchin, Naftali A. Langberg, Frank Proschan

Department of Statistics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	241-256
Number of pages	16
Journal	Statistics and Risk Modeling
Volume	1
Issue number	3
DOIs	https://doi.org/10.1524/strm.1983.1.3.241
State	Published - Mar 1983

Bibliographical note

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

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Statistics, Probability and Uncertainty

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10.1524/strm.1983.1.3.241

Cite this

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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.",

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AU - Langberg, Naftali A.

AU - Proschan, Frank

N1 - Funding Information: Research supported by the Air Force Office of Scientific Research, AFSC,

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AB - 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.

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IS - 3

ER -

A New Method for Estimating Life Distributions from Incomplete Data

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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