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Inference for Stress-Strength Models Based on the Bivariate General Farlie-Gumbel-Morgenstern Distributions |
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PP: 141-150 |
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doi:10.18576/jsapl/070304
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Author(s) |
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Dina Ahmed,
Sohair Khames,
Nahed Mokhli,
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Abstract |
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| In this paper two forms of bivariate distributions are proposed, namely, the Bivariate General Exponential Farlie-Gumbel- Morgenstern (BGE-FGM) form and the Bivariate General Inverse Exponential Farlie-Gumbel-Morgenstern (BGI-FGM) form. Explicit general expressions for the stress-strength reliability R = P(X2 < X1) are obtained, when both the random strength X1 and the random stress X2 are dependent with either BGE-FGM form or BGI-FG form. Also a characterization of the marginal of the bivariate forms is presented associated with R. Three estimators as well as a Bayesian estimator of R are derived. The bivariate Weibull and the bivariate Burr type III FGM distributions are studied as special cases of the bivariate BGE-FGM and the BGI-FGM forms, respectively. A simulation study is carried out to detect the performance of the estimators obtained. Also a real life data example is presented as a practical example of the proposed models. |
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