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Characterizations using the bivariate failure rate function

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  • Navarro, Jorge

Abstract

A general procedure to characterize bivariate absolutely continuous distributions by using the bivariate failure (hazard) rate function is obtained. The theoretical results are illustrated by obtaining new characterizations of some probability models including the bivariate Gumbel exponential and the bivariate Pareto (Lomax) distributions.

Suggested Citation

  • Navarro, Jorge, 2008. "Characterizations using the bivariate failure rate function," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1349-1354, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1349-1354
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    References listed on IDEAS

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    1. Marshall, Albert W., 1975. "Some comments on the hazard gradient," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 293-300, July.
    2. Finkelstein, M. S., 2003. "On one class of bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 1-6, October.
    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. Maxim Finkelstein & Veronica Esaulova, 2005. "On the weak IFR aging of bivariate lifetime distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 21(3), pages 265-272, May.
    5. 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.
    6. Felix Belzunce & Jorge Navarro & José M. Ruiz & Yolanda del Aguila, 2004. "Some results on residual entropy function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 147-161, May.
    7. Nanda, Asok K. & Bhattacharjee, Subarna & Alam, S.S., 2006. "Properties of proportional mean residual life model," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 880-890, May.
    8. Nanda, Asok K. & Bhattacharjee, Subarna & Alam, S.S., 2007. "Properties of aging intensity function," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 365-373, February.
    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.
    10. Jorge Navarro & Jose Ruiz, 2004. "A characterization of the multivariate normal distribution by using the hazard gradient," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 361-367, June.
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    Cited by:

    1. Antonio Di Crescenzo & Franco Pellerey, 2011. "Improving series and parallel systems through mixtures of duplicated dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 411-418, August.
    2. 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.
    3. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "A robust extension of the bivariate Birnbaum–Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 418-435.

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