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Reliability for some bivariate exponential distributions

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  • Saralees Nadarajah
  • Samuel Kotz

Abstract

In the area of stress-strength models, there has been a large amount of work as regards estimation of thereliability 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, forms of R are considered when ( X , Y ) follow bivariate distributions with dependence between X and Y . In particular, explicit expressions for R are derived when the joint distribution isbivariate exponential. The calculations involve the use of special functions. An application of the results is also provided.

Suggested Citation

  • Saralees Nadarajah & Samuel Kotz, 2006. "Reliability for some bivariate exponential distributions," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-14, February.
    • Handle: RePEc:hin:jnlmpe:041652
    DOI: 10.1155/MPE/2006/41652
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    Cited by:

    1. Emrah Altun & Mustafa Ç. Korkmaz & Mahmoud El-Morshedy & Mohamed S. Eliwa, 2021. "A New Flexible Family of Continuous Distributions: The Additive Odd-G Family," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    2. 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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