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Bivariate models from univariate life distributions: A characterization cum modeling approach

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  • Dilip Roy

Abstract

Bivariate life distribution models are of importance for studying interdependent components. We present a generic approach by introducing a new concept of characterized model in stead of a characterized distribution. It strikes a balance between characterization and modeling approaches to eliminate their individual limitations and incorporate their respective strengths. The proposed model, being a characterized one, admits many important properties irrespective of the choice of marginal distributions. The retention of univariate IFR, DFR, IFRA, DFRA, NBU, and NWU class properties in the bivariate setup has been ensured along with some results on series combinations and convolution. No other models, available in the literature, can ensure simultaneous retention of these fundamental and extremely important class properties. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

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  • 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.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:5:p:741-754
    DOI: 10.1002/nav.20027
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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. Roy, Dilip & Gupta, R. P., 1996. "Bivariate Extension of Lomax and Finite Range Distributions through Characterization Approach," Journal of Multivariate Analysis, Elsevier, vol. 59(1), pages 22-33, 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. 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.
    5. Shaked, Moshe, 1982. "A general theory of some positive dependence notions," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 199-218, June.
    6. Roy, Dilip & Mukherjee, S. P., 1998. "Multivariate Extensions of Univariate Life Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 72-79, October.
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