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Reliability for some bivariate beta 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 beta. The calculations involve the use of special functions.

Suggested Citation

  • Saralees Nadarajah, 2005. "Reliability for some bivariate beta distributions," Mathematical Problems in Engineering, Hindawi, vol. 2005, pages 1-11, January.
    • Handle: RePEc:hin:jnlmpe:638187
    DOI: 10.1155/MPE.2005.101
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    Cited by:

    1. Susanne Trick & Constantin A. Rothkopf & Frank Jäkel, 2023. "Parameter estimation for a bivariate beta distribution with arbitrary beta marginals and positive correlation," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 163-180, August.
    2. Jones, M.C., 2022. "Duals of multiplicative relationships involving beta and gamma random variables," Statistics & Probability Letters, Elsevier, vol. 191(C).

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