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Biometrika 1994 81(3):567-577; doi:10.1093/biomet/81.3.567
© 1994 by Biometrika Trust
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Articles

Estimation from quasi life tables

LAURENCE A. BAXTER

Department of Applied Mathematics and Statistics, State University of New York at Stony Brook Stony Brook, New York 11794-3600, U.S.A.

Received for publication 1 March 1993. Revision received 1 November 1993.
  Abstract

A large number of identical components are simultaneously set into operation at each of a regular sequence of times and, on failure, a component is instantaneously replaced. The functional form of the distribution of the component lifelength is assumed to be known and it is desired to estimate the parameters of this distribution. However, no observations of the lifelengths of individual components have been recorded: the only information available is the numbers of components which fail between successive time points. It is shown how this information, in conjunction with the theory of recurrent events, may be used to construct a nonparametric estimator of the discretised lifelength distribution. The latter is then used to estimate the unknown parameters.

Key Words: Least squares estimate • Nonparametric estimate • Probability metric • Recurrent event • Weibull distribution


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