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Reliability for some bivariate gamma distributions

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  • Saralees Nadarajah

Abstract

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr ( X < Y ) . The algebraic form for R = Pr ( X < Y ) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when ( X , Y ) follows a bivariate distribution with dependence between X and Y . In particular, we derive explicit expressions for R when the joint distribution is bivariate gamma. The calculations involve the use of special functions.

Suggested Citation

  • Saralees Nadarajah, 2005. "Reliability for some bivariate gamma distributions," Mathematical Problems in Engineering, Hindawi, vol. 2005, pages 1-13, January.
    • Handle: RePEc:hin:jnlmpe:924843
    DOI: 10.1155/MPE.2005.151
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    Cited by:

    1. Abraão Nascimento & Jodavid Ferreira & Alisson Silva, 2023. "Divergence-based tests for the bivariate gamma distribution applied to polarimetric synthetic aperture radar," Statistical Papers, Springer, vol. 64(5), pages 1439-1463, October.
    2. A. James & N. Chandra & Nicy Sebastian, 2023. "Stress-strength reliability estimation for bivariate copula function with rayleigh marginals," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 196-215, March.
    3. Pushpa Narayan Rathie & Luan Carlos de Sena Monteiro Ozelim & Bernardo Borba de Andrade, 2021. "Portfolio Management of Copula-Dependent Assets Based on P ( Y < X ) Reliability Models: Revisiting Frank Copula and Dagum Distributions," Stats, MDPI, vol. 4(4), pages 1-24, December.

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