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On multivariate mean remaining life functions

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  • Arnold, Barry C.
  • Zahedi, Hassan

Abstract

The concept of the mean remaining life function is extended to the multivariate case. Some general characterization properties of multivariate mean remaning life functions (mmrl) are studied, it is shown that they determine the joint pdf uniquely. Inter alia a basic convergence result is proved for a sequence of mmrl functions. The multivariate loss of memory property of a pdf is characterized in terms of the mmrl function. The relationship between the mmrl function and the hazard-gradient is discussed.

Suggested Citation

  • Arnold, Barry C. & Zahedi, Hassan, 1988. "On multivariate mean remaining life functions," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 1-9, April.
    • Handle: RePEc:eee:jmvana:v:25:y:1988:i:1:p:1-9
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    Cited by:

    1. S. Ashrafi & M. Asadi, 2015. "On the stochastic and dependence properties of the three-state systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 261-281, April.
    2. Paduthol Gaduthol Sankaran & Bovas Abraham & Ansa Alphonsa Antony, 2006. "A dependence measure for bivariate failure time data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 327-341.
    3. Kumar Gupta, Sanjib & De, Soumen & Chatterjee, Aditya, 2017. "Some reliability issues for incomplete two-dimensional warranty claims data," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 64-77.
    4. Rojo, Javier & Ghebremichael, Musie, 2006. "Estimation of two ordered bivariate mean residual life functions," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 431-454, February.
    5. V. N. Sreeja & P. G. Sankaran, 2007. "Proportional mean residual life model for gap time distributions of recurrent events," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 319-336.
    6. Hu, Taizhong & Khaledi, Baha-Eldin & Shaked, Moshe, 2003. "Multivariate hazard rate orders," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 173-189, January.
    7. Paduthol Godan Sankaran & Narayanan Unnikrishnan Nair, 2004. "Partial moments for bivariate distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 339-351.

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