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Some comments on the hazard gradient

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  • Marshall, Albert W.

Abstract

For random variables T1,...,Tn, the gradient of R(t) = -logP{T1 > t1,...,Tn > tn} is called the hazard gradient. Some properties of this multivariate version of the hazard rate are demonstrated, and some examples are given to show the usefulness of the hazard gradient in characterizing distributions or families of distributions.

Suggested Citation

  • Marshall, Albert W., 1975. "Some comments on the hazard gradient," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 293-300, July.
    • Handle: RePEc:eee:spapps:v:3:y:1975:i:3:p:293-300
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    Cited by:

    1. Navarro, Jorge, 2008. "Characterizations using the bivariate failure rate function," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1349-1354, September.
    2. Jayme Pinto & Nikolai Kolev, 2016. "A class of continuous bivariate distributions with linear sum of hazard gradient components," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-17, December.
    3. Pinto, Jayme & Kolev, Nikolai, 2015. "Sibuya-type bivariate lack of memory property," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 119-128.
    4. Ebrahim Amini-Seresht & Baha-Eldin Khaledi, 2015. "Multivariate stochastic comparisons of mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 1015-1034, November.
    5. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    6. Li, Tao & Sethi, Suresh P. & Zhang, Jun, 2014. "Supply diversification with isoelastic demand," International Journal of Production Economics, Elsevier, vol. 157(C), pages 2-6.
    7. Marshall, Albert W. & Olkin, Ingram, 2015. "A bivariate Gompertz–Makeham life distribution," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 219-226.
    8. Hu, Taizhong & Khaledi, Baha-Eldin & Shaked, Moshe, 2003. "Multivariate hazard rate orders," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 173-189, January.
    9. Gupta, Pushpa L. & Gupta, Ramesh C., 1997. "On the Multivariate Normal Hazard," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 64-73, July.
    10. Kotz, Samuel & Navarro, Jorge & Ruiz, Jose M., 2007. "Characterizations of Arnold and Strauss' and related bivariate exponential models," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1494-1507, August.
    11. 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.
    12. Guillermo Martínez-Flórez & Carlos Barrera-Causil & Artur J. Lemonte, 2022. "Power Families of Bivariate Proportional Hazard Models," Mathematics, MDPI, vol. 10(23), pages 1-18, November.
    13. Debasis Kundu & Rameshwar Gupta, 2011. "Absolute continuous bivariate generalized exponential distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(2), pages 169-185, June.
    14. Basu, Asit P. & Sun, Kai, 1997. "Multivariate Exponential Distributions with Constant Failure Rates," Journal of Multivariate Analysis, Elsevier, vol. 61(2), pages 159-169, May.
    15. Dilip Roy, 2004. "Bivariate models from univariate life distributions: A characterization cum modeling approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(5), pages 741-754, August.

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    Keywords

    hazard rate hazard gradient;

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