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Estimation of parameters in logistic and log-logistic distribution with grouped data

Lifetime Data Analysis volume 13, pages 421–429 (2007)Cite this article

Abstract

In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration is the log-logistic distribution. This paper demonstrates the existence and uniqueness of the MLEs of the parameters of the logistic distribution under mild conditions with grouped data. The times with the maximum failure rate and the mode of the p.d.f. of the log-logistic distribution are also estimated based on the MLEs. The methodology is further studied with simulations and exemplified with a data set with artificially introduced grouping from a locomotive life test study.

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Affiliations

  1. Department of Statistics, Florida International University, 11200 SW 8th Street, Miami, FL, 33199, USA

    Yan Yan Zhou, Jie Mi & Shengru Guo

Authors
  1. Yan Yan Zhou
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  2. Jie Mi
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  3. Shengru Guo
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Correspondence to Yan Yan Zhou.

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Zhou, Y.Y., Mi, J. & Guo, S. Estimation of parameters in logistic and log-logistic distribution with grouped data. Lifetime Data Anal 13, 421–429 (2007). https://doi.org/10.1007/s10985-007-9038-0

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  • DOI: https://doi.org/10.1007/s10985-007-9038-0

Keywords

  • Log-logistic distribution
  • Grouped sample
  • Maximum likelihood estimators
  • Failure rate
  • mode