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Preservation properties for the Laplace transform ordering of residual lives

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Abstract

Several preservation results for the Laplace transform ordering of residual lives (Lt−rl) are given. In particular, we show that theTt−rl-order is preserved under convolutions, mixtures and weak convergence. Some examples of interest in reliability theory are also presented.

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References

  • Alzaid, A., Kim, J. and Proschan, F. (1991). Laplace ordering and its application.Journal of Applied Probability,28, 116–130.

    Article  MATH  MathSciNet  Google Scholar 

  • Barlow, R. and Proschan, F. (1981).Statistical Theory of Reliability and Life Testing, To Begin with, Silver Spring, MD.

  • Belzunce, F., Ortega E. and Ruiz J. (1999). The Laplace order and ordering of residual lives.Statistics & Probability Letters,42, 145–156.

    Article  MATH  MathSciNet  Google Scholar 

  • Karlin, S. (1968).Total Positivity, Vol. I. Stanford University Press, Stanford, CA.

    MATH  Google Scholar 

  • Klefsjo, B. (1983). A useful ageing property based on the Laplace transform.Journal of Applied Probability,20, 615–626.

    Article  MathSciNet  Google Scholar 

  • Shaked, M., Shanthikumar, J. G. (1994).Stochastic Orders and their Applications. Academic Press, New York.

    MATH  Google Scholar 

  • Shaked, M. and Wong, T. (1997). Stochastic orders based on ratios of Laplace transforms.Journal of Applied Probability,34, 404–419.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. The Institute of Statistical Studies and Research, Cairo University, Egypt

    Hadi Ahmed

  2. Faculty of Education (Suez), Suez Canal University, Egypt

    Mohamed Kayid

Authors
  1. Hadi Ahmed
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  2. Mohamed Kayid
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Ahmed, H., Kayid, M. Preservation properties for the Laplace transform ordering of residual lives. Statistical Papers 45, 583–590 (2004). https://doi.org/10.1007/BF02760570

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  • DOI: https://doi.org/10.1007/BF02760570

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