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Reliability properties of bivariate conditional proportional hazard rate models

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  • Navarro, Jorge
  • Sarabia, José María

Abstract

In this paper, we study reliability properties in two classes of bivariate continuous distributions based on specification of conditional hazard functions. These classes were constructed by conditioning on two different kinds of events in Arnold and Kim [6]. Several reliability properties are studied here including survival and hazard bivariate functions, hazard components, the Clayton–Oakes measure, and conditional densities and hazard rate functions of the marginal and conditional distributions. We also study properties for the series and parallel systems with component lifetimes having these particular dependence models.

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  • Navarro, Jorge & Sarabia, José María, 2013. "Reliability properties of bivariate conditional proportional hazard rate models," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 116-127.
    • Handle: RePEc:eee:jmvana:v:113:y:2013:i:c:p:116-127
    DOI: 10.1016/j.jmva.2011.03.009
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    References listed on IDEAS

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    1. Ramesh C. Gupta, 2006. "Reliability studies of bivariate distributions with Pearson type VII conditionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 239-251.
    2. Arnold, Barry C., 1987. "Bivariate distributions with pareto conditionals," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 263-266, June.
    3. Gupta, Ramesh C., 2001. "Reliability Studies of Bivariate Distributions with Pareto Conditionals," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 214-225, February.
    4. Jorge Navarro & Moshe Shaked, 2010. "Some properties of the minimum and the maximum of random variables with joint logconcave distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 313-317, May.
    5. Jorge Navarro & José Ruiz & Carlos Sandoval, 2006. "Reliability properties of systems with exchangeable components and exponential conditional distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 471-484, September.
    6. Navarro, Jorge, 2008. "Characterizations using the bivariate failure rate function," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1349-1354, September.
    7. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
    8. 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.
    9. Shanbhag, D. N. & Kotz, S., 1987. "Some new approaches to multivariate probability distributions," Journal of Multivariate Analysis, Elsevier, vol. 22(2), pages 189-211, August.
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    Cited by:

    1. J. Navarro & M. Esna-Ashari & M. Asadi & J. Sarabia, 2015. "Bivariate distributions with conditionals satisfying the proportional generalized odds rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 691-709, August.
    2. Arnold, Barry C. & Sarabia, José María, 2022. "Conditional specification of statistical models: Classical models, new developments and challenges," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Vilca, Filidor & Romeiro, Renata G. & Balakrishnan, N., 2016. "A bivariate Birnbaum–Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 169-183.
    4. Kolev, Nikolai, 2016. "Characterizations of the class of bivariate Gompertz distributions," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 173-179.
    5. Rajesh, G. & Abdul-Sathar, E.I. & Maya, R., 2015. "Local linear estimation of residual entropy function of conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 1-14.

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