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Estimation in a Model of Sequential Order Statistics with Ordered Hazard Rates

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Ordered Data Analysis, Modeling and Health Research Methods

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 149))

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Abstract

As a generalization of order statistics from independent and identically distributed random variables, sequential order statistics (SOSs) may be applied as a model for ordered data, when assuming changes of underlying distributions immediately after the occurrences of ordered observations. For example, in the case of a model for k-out-of- n-systems , where the \(n-k+1\) failures of components in a system of n components occur successively, a change of the respective underlying distribution after a failure is motivated by an increased load put on the remaining components. The corresponding cumulative distribution functions are assumed to have possibly different ordered hazard rates, which are further multiplied by factors, in order to build the hazard rates of the SOSs. These factors are the parameters of interest. Estimation of the parameters is considered by means of maximum likelihood under order restriction, by means of link functions, and in a Bayesian set-up with an order statistics prior .

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Author information

Authors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Marco Burkschat, Udo Kamps & Maria Kateri

Authors
  1. Marco Burkschat
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  2. Udo Kamps
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  3. Maria Kateri
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Corresponding author

Correspondence to Udo Kamps .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences FO 35, University of Texas at Dallas, Richardson, Texas, USA

    Pankaj Choudhary

  2. Fordham University, New York, New York, USA

    Chaitra H. Nagaraja

  3. Southern Methodist University, Dallas, Texas, USA

    Hon Keung Tony Ng

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Burkschat, M., Kamps, U., Kateri, M. (2015). Estimation in a Model of Sequential Order Statistics with Ordered Hazard Rates . In: Choudhary, P., Nagaraja, C., Ng, H. (eds) Ordered Data Analysis, Modeling and Health Research Methods. Springer Proceedings in Mathematics & Statistics, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-319-25433-3_7

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