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Reliability Studies of Bivariate Distributions with Pareto Conditionals

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  • Gupta, Ramesh C.

Abstract

In this paper we study Arnold's (1987, Statist. Probab. Lett.5, 263-266) class of bivariate distributions with Pareto conditionals from a reliability point of view. Failure rates and mean residual life function of the marginal distributions and their monotonic properties are studied. The hazard components and their properties are investigated and their relationships with some measures of dependence are established. Finally, the failure rate of the minimum of the two components is examined and its monotonicity is investigated. Some of the results presented here are general and would be useful in studying the dependence structure in other classes of bivariate distributions.

Suggested Citation

  • Gupta, Ramesh C., 2001. "Reliability Studies of Bivariate Distributions with Pareto Conditionals," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 214-225, February.
    • Handle: RePEc:eee:jmvana:v:76:y:2001:i:2:p:214-225
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    References listed on IDEAS

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    1. Arnold, Barry C., 1987. "Bivariate distributions with pareto conditionals," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 263-266, June.
    2. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose María, 1993. "Multivariate distributions with generalized Pareto conditionals," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 361-368, August.
    3. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
    4. E. Castillo & J. Galambos, 1989. "Conditional distributions and the bivariate normal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 209-214, December.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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