Statistical Papers

, Volume 60, Issue 1, pp 53–72 | Cite as

Stochastic properties of a weighted frailty model

  • J. JarrahiferizEmail author
  • M. Kayid
  • S. Izadkhah
Regular Article


This paper is intended to consider a weighted proportional hazards model and the arising mixture model from it which is called weighted frailty model and study some properties in the context of reliability theory. It is shown that the frailty random variable and the population level variable are negatively likelihood ratio dependent. Closure properties of the model with respect to some stochastic orders and some aging classes of life distributions are investigated. Finally, preservation of some stochastic orders under the structure of the model is studied. Various illustrative examples are also given.


Hazard rate Weighted distribution Preservation Stochastic order Aging class 

Mathematics Subject Classification

Primary 60E15 Secondary 60K10 62N05 



The authors are grateful to two referees for their constructive comments which lead to the current improved version. The second author would like to extend his sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this Research Group No. (RGP-1435-036).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Birjand BranchIslamic Azad UniversityBirjandIran
  2. 2.Department of Mathematics, Faculty of ScienceSuez UniversitySuezEgypt
  3. 3.Department of Statistics and Operations Research, College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  4. 4.Department of Statistics, Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran

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