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Representation of Downton’s bivariate exponential random vector and its applications

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  • Kim, Bara
  • Kim, Jeongsim

Abstract

Downton’s bivariate exponential distribution is one of the most important bivariate distributions in reliability theory. In this paper a simple representation for Downton’s bivariate exponential random vector is given. As an application of this representation, we consider a reliability model where an item is subject to shocks and obtain an explicit expression for the long-run cost rate.

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  • Kim, Bara & Kim, Jeongsim, 2011. "Representation of Downton’s bivariate exponential random vector and its applications," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1743-1750.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1743-1750
    DOI: 10.1016/j.spl.2011.07.013
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    References listed on IDEAS

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    1. A. J. Lawrance & P. A. W. Lewis, 1983. "Simple Dependent Pairs of Exponential and Uniform Random Variables," Operations Research, INFORMS, vol. 31(6), pages 1179-1197, December.
    2. V. Barnett, 1985. "The Bivariate Exponential Distribution; A Review And Some New Results," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 39(4), pages 343-356, December.
    3. 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.
    4. Wang, Rong-Tsorng, 2007. "A reliability model for multivariate exponential distributions," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 1033-1042, May.
    5. 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.
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    Cited by:

    1. Hüseyin Sarper, 2019. "Correlated reliability and an application: Propulsive landing on Mars," Journal of Risk and Reliability, , vol. 233(5), pages 826-846, October.
    2. Kim, Hwa-Sung & Kim, Bara & Kim, Jerim, 2014. "Pricing perpetual American CatEPut options when stock prices are correlated with catastrophe losses," Economic Modelling, Elsevier, vol. 41(C), pages 15-22.

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