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A note on closure of the ILR and DLR classes under formation of coherent systems

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Abstract

In this paper, we give the closure of the class of increasing likelihood ratio (ILR) life distributions under the formation of certain coherent systems with independent and identically distributed components, and particularly in k-out-of-n systems. Some possible definitions of its dual class (DLR) are discussed and results about the closure are given. Furthermore, we include examples which show that these two aging classes are not closed under formation of special coherent systems.

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Authors and Affiliations

  1. Departmento Estadistica e I.O., Universidad de Murcia, 30100, Murcia, Spain

    Manuel Franco

  2. Departmento Matematica Aplicada y Estadistica, Universitat Politécnica de Cartagena, 30203, Murcia, Spain

    M. Carmen Ruiz & José M. Ruiz

Authors
  1. Manuel Franco
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  2. M. Carmen Ruiz
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  3. José M. Ruiz
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Additional information

This work has been supported by Ministerio de Ciencia y Tecnologia, Grants PB96-1105 and BFM2000-0362.

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Franco, M., Ruiz, M.C. & Ruiz, J.M. A note on closure of the ILR and DLR classes under formation of coherent systems. Statistical Papers 44, 279–288 (2003). https://doi.org/10.1007/s00362-003-0152-0

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  • DOI: https://doi.org/10.1007/s00362-003-0152-0

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