Journal of Statistics Applications & Probability

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In this paper, the estimation of R = P [Y < X], namely Stress- Strength model is studied when both X and Y are two independent random variables with the extended linear exponential distribution (ELED), under different assumptions about their parameters, Maximum likelihood estimator in the case of fixed two parameters (π‘Ž=1,𝑏= 2), common unknown parameters (π‘Ž1=π‘Ž2=π‘Ž,𝑏1=𝑏2=𝑏), and all unknown parameters (π‘Ž1,π‘Ž2,𝑏1,𝑏2,𝛼,𝛽) can also be obtained in explicit form. Estimating R with Bayes estimator with non-informative prior in the same previous cases with the same parameters , we obtain the asymptotic distribution of the maximum likelihood estimator and it can be used to construct confidence interval of R. Different methods are compared using simulations and one data analysis has been performed for illustrative purposes.

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